If this were my car one of the first test I would do is to
CONFIRM the ability of the grounds to actually carry a heavy current. For the 1999 Convertible is the GEM pin #14 (black) wire which is grounded via G400 (located in the trunk).
In addition to checking and cleaning G400 I would also clean the grounds around the radiator core support and the battery negative. Pay special attention to the negative battery terminal itself since it is bad about splitting.
Once the grounds are known to be clean and tight then measure the voltage drop during window operation between GEM #14 (black) all the way back to battery negative. Here's some information on how to measure voltage drop.
Note, the purpose is to measure the ability of the ground to carry current. The test can be done with the windows going up or down.
Optionally a test light with the pig tail extended to battery positive could be used to perform a basic check of the ground's ability to carry ground.
Another method is to use a scrap piece of wire as a jumper between the GEM ground connector terminals back to battery negative. IF this restores function then this tells you that you are on the right track.
Howto perform charging system voltage drop test
https://www.stangnet.com/mustang-fo...perform-charging-system-voltage-drop-test.56/
Also please note that the power windows are protected by an automatic resetting circuit breaker. The CB is located in the Central junction box as well as the window motor itself. This offers an explanation of how it's possible for the windows to work sometimes and not others.
It might also be possible to bypass the GEM by jumping terminals #1 (TN/LB) and #4(WH/BK). However please note that I have no direct knowledge this will work. Do this at your own risk. Suggest using a fused jump wire to protect the electronics.
Another option is to de-pin GEM #1 and #4 and connect together. This will bypass the GEM completely. Maybe consider de-pinning #14 just to be safe. Recommending doing this only after you are positive the problem is actually in the GEM. Again at your own risk.