Electric Start issue

[bret]

When I touch the screwdriver from the metal part under the red cap to where the flathead part is touching, the electric starter fires up and starts the bike. The problem is, the "start" button doesn't work. What do I need to do to get it to work?

 

[XSLeo]

Ok, the starter relay, the thing you bypassed by jumping across the cables. It has two small wires, one re/white the other blue/white.
You should get battery voltage one the red/white wire with the key and engine stop switch in the run position. If not trace the red/white wire to see where the voltage gets lost.
The blue white wire goes up to the push button where the button grounds the b/w wire to the switch housing. On your 81 the ground path for the switch housing is to the bars, over to the left side switch housing where a black wire carries it to the harness ground in the headlight bucket.
A few tests you can try after you get battery voltage to the red/white wire is to unplug the blue/white wire, jumper from this wire to ground. This should trip the relay and crank the starter. If it does plug the wire back in. Remove the right side switch housing. Find the blue/white wire. Jumper it to ground. If the starter works, the push button may be dirty or the connection between the button and housing may be dirty.
Clean things up.
Reassemble the housing to the bars being sure that the steel tab in the housing has a good clean bare metal to bare metal connection. If the bars are painted or powder coated, you need to grind away to bare metal. The same on the left housing. Once you get a good ground path the starter will work.
Leo