Good day all been awhile since I've been on.
Busted out my 92 gs (been in the garage collecting dust for a couple years) was giving it a good look over checking fuels and such, cleaned her up and went to go for a little putt putt. After letting her idle for a few minutes noticed smoke and electrical burn smell and find my positive lead from the solenoid to battery was melting. Replaced with new solenoid and wire but still doing the same thing. Any ideas?

Wow!

Don't see that happen too often because usually the main fuse would blow out. You need to get an ammeter hooked up in series with the negative ground cable and if possible use a relay/fuse device. Turn on ignition switch, watch the ammeter draw, then start disconnecting stuff until you find the draw.

Of course, another way is to do a visual inspection of all electrical components, see if you can find the short circuit, possible wires where they exit the ignition switch, wires that pass by the steering head, wires to the rectifier regulator.

Ammeter could be a bulb in series. It prevents a short circuit and limits the current.
A multimeter to check resistance also works.
Hot wire  from battery is directly connected to one end of the starter relay with no fuse, fuse starts from there to ignition switch, only possibility to imagine that is the starter motor is blocked or in shortcircuit and the solenoid is stuck closing the circuit causing infinite consumption.
You changed the starter solenoid.
Without connecting the starter motor ( disconnect other end of relay, thick wire to starter) it clicks when pushing engine start switch?
Maybe the relay is always energized via the switch (two little wires,round bullet connector)
I would check the starter electrical motor. Positive wire, resistance to ground. Service manual states typical resistance.
Open the metal plate covering the starter motor and  inspect the cables (2 8mm hex screws)

"Hot wire  from battery is directly connected to one end of the starter relay with no fuse, fuse starts from there to ignition switch, only possibility to imagine that is the starter motor is blocked or in shortcircuit and the solenoid is stuck closing the circuit causing infinite consumption."

Yes, I see that now. Suggest a close look at the starter especailly where the cable connects, there are usually a few special washers that isolate the cable from the starter body. Otherwise, look inside starter for short to ground.