On the PRO-651 if you adjust the expert setting "RF SQ Fade" to a very small number like 0 or 1 you will all but eliminate the squelch tail. For some reason, and I can't remember why, I have it set to 1 and not 0. So you'll have to experiment to see which works best for you.
On the WS1080/TRX-1 there are no settings to adjust the squelch tail. I'm not sure why GRE did not incorporate these settings into their PSR-800 when they originally designed it. (The Radio Shack PRO-18 & PRO-668 as well as the Whistler WS1080,WS1088 and TRX-1 are all decendents.) Maybe there is a dedicated IC just for analog squelch detection? In the PSR-500 the analog squelch detection was handled by the DSP so it could be adjusted. (The PRO-651 is one of the many decendents of that radio.) I have never been curious enough to look into it it further. But it was one of the annoyances that I had with my TRX-1 when I had one.