Trans swap wouldn't cause that to happen. Did you swap the ECM or chip to the 5 speed version? If not the shift light will function as if you still had a 4 speed when you actually have an extra gear to shift. That still wouldn't cause it to come on when checking for codes. Seems like you had this issue before the trans swap.
Pull your console and look at the ECM harness for any splices. You can also pull the dash cluster and look for the same. Something unusual is going on here.
If someone chimes in and suggest swapping the 2 bulbs (shift - Chk Eng) don't fall for it. Or try swapping the 4 spd back in to see if it makes a difference..
Let us know how you make out. Look up the wiring diagram and get a multi-meter.
"Kilgore Trout once wrote a short story which was a dialogue between two pieces of yeast. They were discussing the possible purposes of life as they ate sugar and suffocated in their own excrement. Because of their limited intelligence, they never came close to guessing that they were making champagne." - Kurt Vonnegut