Hi,
I've both a TL866CS and a GQ-4X (and some others ... ).

The GQ-4X should be able to burn the old TMS2532. Never tried it, but my experience it that all chips announced by Mcumall have been really tested (not like some chineese programmer like Top series....).
The GQ-4X can burn the old 2716 and 2732 at 25v without problem, of course it need an external power connected, but it works fine. Same for the A version (21v) or B (12.7v).
2017-12-29_19h45_20 (resized).png
As you know, the pinout of the 2532 from Texas Instrument is a little bit different from the 2732.
Looking at the software option, the GQ-4X has the ability to program the 2532.
But only read the 2532A.
2017-12-29_20h14_22 (resized).png
May be you can take a look at the Mcumall forum, there is a topic about 2532 programming here:
http://www.mcumall.com/forum/topic.asp?TOPIC_ID=2917

This seems to confirm that the 2532 @ 25 volts can be programmed, from Texas (TMS2532) or Hitachi (HN462532), but the 2532A can only be read with the GQ-4X.
Note : keep your TL866CS - it's a good device that work fine, but has some limitation (no more than 21v VPP). The GQ-4X can't program the PAL/GAL (sometime used in pinballs), but the TL866CS can.

I've never encounter problems with GAL programming with my TL866CS. I use often GAL 16V8D from Lattice (some -15, some -25) and also ATMEL AT16V8B, no problem at all with that.
Fun ... I've also tried the "ST M2732A Singapore/China" from Ebay. The announce said Vpp 21 volts, but I receive this set (I also order 27C128) with a strange marking : Pgm 12.5v printed on it
DSC03188 (resized).JPG
But the seller was serious, and he clearly announced that the chip was really 21 volts and there was an error on the label print.
In the 80's, I've programmed many 2716 and 2732, and for me, it's obvious that a 2732A is @ 21 volts and only special/cmos can be 12.5v !
But as I'm curious, I first give it a try @ 12.5v - of course, this doesn't works.

But at 21v, as expected - this M2732A program perfectly and also fast ! (I select AT2732 on Miniprog, and set Vpp to 21 volts).
The M27C128 program also fine and fast (I select AM27C128 and uncheck the "check-id" box).
So, for me, there is no problem with this kind of memories.