Ugh.
Let's back up. The fact that the fluid was nasty tells me there was a lack of maintenance by the PO. That, coupled with likely overheating, kills the harness clips and fasteners (and sometimes the wires themselves).
Faint click indicates a functional solenoid.
I'm not sure how voltage-sensitive each wire is - I'd suspect not very, in '98. Your marine-style splices should be sufficient. Mechanically, 200k is about the limit for most automatic trans lifespans - It's a shame that yours might be done in by the actual harness or something electrical.