99 Pontiac Bonneville se .... has anyone ever re-soldered their own ABS control module? If so how exactly did you do it? I see YouTube videos on doing it yourself. Finally what is the make and model for my particular ABS module?

As tempting as it is, I haven't done so myself.
Opted for a used module off Ebay, since Andrew (Harofreak00) didn't have the one needed for my 2001.

As for module numbers, it depends on the options that your vehicle has. I think there are only 2 types but am not 100% sure--with or without traction control.
Best bet is to get a close look and either copy all the numbers from the EBCM label or just snap a pic.

If your Bonnie doesn't have traction control, the Rockauto does not have a remanufactured unit for you.

Search past threads and you might find repair experiences.

Just out of curiosity, is this just fixing broken wiring or something else?

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95 SLE... a keeper. 241k miles. Low and Slow.
97 BMW 528i
98 Infiniti vq35'd i30: 13.3@104mph, 30MPG Hwy (RIP)
02 Jag X-type
03 BMW M5
05 Chevy Cobalt LS
07 Infiniti G35s 6MT (Sold)
07 Ducati Monster S2R 800 with DS1000 swap
83 Yamaha IT175K
72 Yamaha DS7: '74 RD250 swap, JL chambers

Info on dropping a 92-99: Here.

Typically, the issue is internal; one or more bad solder joints.