05 Z71 Batter light on

[onebad65c10]

Good day all. Have a quick question that maybe I can get a bit of help with.
Have an 05 Silverado Z71 Extended cab 5.3 vin T. A couple of months ago I developed some alternator noise. Was led to a faulty Alt. 240k on original one. Swapped out with a parts store unit. After a week my Optima red top died. Check with diag machine at work and found a bad cell. Swapped with battery from my other truck. All good Battery and alt output checked out good. Only problem is now my battery light is on. Steadily illuminated and goes off when truck is off. Checked battery voltage and 13.4 @idle and 13.7 with loads and revving. No codes for charging system present. No parasitic draw present.
Checked wire B9 at cluster connector and voltage present.
Checked the brown wire at the back of the alternator and I have a ground on that wire plugged, unplugged and while running.
Was wondering if since the truck is charging and reading voltage within spec i this was a problem in the cluster or something else going on. Any help would be greatly appreciated.
Thank you,
Phil

[homemade87]

Its probably the regulator in the alternator . Thats what controls the light . 13.4 seens a little low to me . It should be around 13.8 to 14.3 . I would swap the alt out . Could have been part of the battery problem .