I have the same problem. I found an adjustment in the shifter. Take the cover off the shifter and look inside. Watch it as you move the shifter in and out of reverse and you will see the little switch that it hits. You carefully and you will see the adjustment.
I'm at work now but can take some photos this evening.
However, I adjusted the switch but it was not enough. It is better, but I still need to hold the shifter over to get the light on. I need to adjust it again, after I replace the leaking coolant hose this weekend.
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Jim Martin
White '86 GT
California