when I fab and install a battery ground cable I always go to the frame and the engine block. the biggest draw in the system will be the starter which is bolted to the engine block or the transmission so that is the first run from the battery. from that bolt on the engine I also attach a cable that goes to the frame. the frame is a front to rear conduit for other grounds for lights etc. from there I install a ground from the frame to the sheet metal stuff like the cab, box, rad support etc as needed. when I am wiring a unit from scratch I do this as well but always try to run a dedicated ground wire for the accy that are outside the cab.
a regular old fashioned test light with a filament style bulb is simply a bulb with a wire and ground clamp connected to one side of the bulb and a sharp probe connected to the other side. since the filament inside the bulb could care less which side is positive and which is negative you can connect them whichever way you need to for your test purposes. these draw more than an led test light will. led test lights are polarity sensitive so you need to connect the ground to the negative side of things if doing a test using the tester inline with the circuit but not connected to a dedicated frame ground, say. old styles testers can sometimes draw more than the circuit in a newer style vehicle is made to handle so the led testers, or a multimeter, are recommended.
how to use a multimeter. if buying one try to get one that will also have provisions for an alligator style clamp so you can clamp it onto a wire or a ground point
https://www.youtube.com/watch?v=c9KNAIjoEYs
on your truck
I would start by checking
-the light assembly to ensure the bulb has a good contact with the bulb holder and the contacts under the bulb are shiny and the spring that keeps pressure on the bulb is still working and not hung up. when you insert the bulb there should be some resistance felt and once in place the bulb should be held against the socket by 2 little pins in the socket slots. this ensure a good connection between the bulb and the socket which is the ground for the bulb.
-compare the new led bulb with an old bulb from the style of bulb holder you have. if it has marker lights and signal lights then it will have 2 contacts and will likely be an 1157. if ity is a single circuit then the bulb may have been an 1156. these bulbs have a couple of little pins that help align the bulb in the holder so the bulb contacts sit in the correct spot to line up with the appropriate contact in the bulb holder. on the double element/circuit bulb (1157) one of these pins sits deeper down on the barrel of the bulb than the other one does. I have had new bulbs from a reputable supplier where the pins were reversed so marker was signals and vice versa or they were totally not in the right spot so both contacts on the bottom of the bulb hit both contacts on the pigtail.
-check for voltage at the light, down inside the light socket but be sure to wrap the tester bare metal parts first with tape, with the bulb removed (or remove the bulb and pull the pigtail wires up through the bulb holder so you can get a better connection without possibly grounding your tester on the bulb holder). ensure you connect your ground first to the frame to get actual voltage available, then do the same test with the ground attached to the bulb socket and see if there is a voltage drop in the circuit which could indicate a poor ground. see what you have for voltage with the engine off-lights on, then signals on, then start the engine and see what you have for the same tests. also check battery voltage not running and then running and compare these results. it's good to write your finding down when you do these tests.
-check the light for a good ground. since both lights are doing it and only since you swapped out to the led bulbs it seems like the problem could be something didn't like being disturbed and a poor connection was the result. I would say that possibly you have a grounding problem on the front sheet metal somewhere or from the bulb holder to the ground. possibly the flasher you have is made to do rapid flashing and does so when the engine is running because the voltage is higher and can overcome some voltage drop from a poor ground. what you may try is a simple jumper wire or booster cable from the battery or the frame over to the front sheet metal where the lights are getting their ground from, like right on the screw head if possible. if the lights have a ground that relies on sheet metal for a connection, like a rad support is common on a lot of these trucks, then that sheet metal needs to be connected to the frame somehow. just grounding the cab and not the front fender or rad support where the light is grounded means the ground needs to go from the battery to the frame or engine then to the cab then through the cab to a fender or inner fender mounting bolt then through that to a rad support bolt so the light can get a ground finally. there are lots of places for the circuit to develop resistance through all those connections. personally, when I wire a light, I try to get a dedicated ground for the light's ground wire. if it's a front signal light like this I will extend the ground wire on the light so it reaches the truck frame rather than ground it on the sheet metal. if the bulb socket relies on the sheet metal body of the light for a ground then I will attach a ground wire to the light housing or the bulb socket housing if possible and then run a ground to the frame. firstly because I want a good ground and secondly because I hate making a screw hole in the sheet metal that will inevitably become a rusty screw hole and a poor connection. on the frame I will buff it down to bare metal, attach the ground wire(s) with a star washer under the wire or under the head of the bolt. I use plated fasteners and try to use a bolt and nut rather than a screw and then when I am done the project, it is tested and found operational, I coat the connection with high zinc paint like weld through primer or I use aviation form a gasket to coat all the surfaces.
-if all seems to be good you could try removing the flasher unit and installing a jumper wire where the power and load terminals are in the flasher bracket. this will eliminate the flasher so when the signals are turned on the signal bulbs will simply come on and not flash. you can try this with the engine running or not.
key off, the signals should not flash, just the 4 ways, head and tail lights and the brake lights should operate.