i had problems with my e-brake light for a while butnot quite what you describe...actually, i have had 2 e-brake experiences here they are:
1) 1993 sport. when i bought it, it needed a brake job and the e-brake was inop. 900 bucks later, i got it back. at first, when the e-brake was applied, no light . then sometimes it would and sometimes it wouldnt. now, it always does. my guess, sticky sensor from lack of use. bought @ 79k, now has 97k
2) 1991 eddie. truck has a bad ABS sensor on rear, causing ABS to not work. someimtes when you brake, no lights. but if you brake hard, or are in traffic, the Rear ABS (it doesnt have 4wABS) and the e-brake light eom on and stay on. the truck does brake just fine, but dont expect to have ABS. truck has 165k buthas done this since bought @ 80k, and as mentioned, culprit is bad ABS sensor.
hope those help ya.