I thought that replacing the (727) trans switch would surely solve this problem in my '70 convert... so I did that, and they STILL stay on in Drive, 2nd, 1st. I checked the wires underneath the car and they don't appear grounded... What next??

That IS a nice ride . pull the connector back off of the 3 pin switch on the trans and (1) see if there is continuity (ohm it) between the 2 outer male pins (key on/trans in any gear except reverse). if yes the problem is in the switch or the rooster comb inside the trans and there was something about some aftermarket switches the contact that touches the comb is too long or too short I forget which caused a similar/related problem but since the other switch you replaced there was the same issue I'll assume that that (wrong/bad switch) ain't an issue. (2) if no continuity see if both outer female cavities in the connector have fire (key on) & one should & the other should not but if it does then there's continuity right there in the connector (not likely) or there's a wiring problem upstream (start at the bulkhead) thats feeding current to the one outer pin wire that goes to the reverse lights as only the switch should be connecting the two outer pins. The center pin if for the NSS & ain't involved in this so leave it alone. www.mymopar.com has the colors

With the lights on in a forward gear unplug the switch. If the lights go out the problem is internal. Only reason I say that is two switches are doing the same thing. 68 and older valve bodies have a different rooster comb. Any chance that your valve body has been replaced?

THANKS for your replies! The reverse lights go out with the switch unplugged... I don't know if anythnig has ever been done with the vavlvebody, the trans has performed 100% in the 14 years I've owned this car.

Inside the trans there is a plastic shoe that sometimes breaks off...this will allow the BU lights to be on in gears other than Reverse.