The fuel shutoff solenoid has 3 wires. White, red and black. Black is ground, white (larger wire) is the pull in circuit and red is the hold in wire. During the PULL IN of solenoid, the white AND the red are engergized. This could amount to about 20 to 25 amps until the PULL IN circuit (white wire) is cut off by releasing the key to run position. You are correct that the wires for the fuel PULL IN and starter solenoid are the same circuit. So something is drawing more amps than normal. I would suspect the fuel solenoid as this is the most common part to fail. The only way to know for sure is to test the circuits with an amp probe to confirm. Also check the plug at back of key switch for a bad connection/corrosion.
This also maybe a handy test to do if you have a meter...
Fuel Shutoff Solenoid Test
Reason:
To verify fuel shutoff solenoid is functioning properly.
Equipment:
Ohmmeter
Procedure:
1. Park machine on level surface with key switch off.
2. Lock park brake.
3. Disconnect fuel shutoff solenoid connector.
MIF
4. Measure and record the resistance across each combination of terminals as listed below.
Fuel Shutoff Solenoid Continuity:
A (Blk) to C (Wht) 0.4 ohms
A (Blk) to B (Red) 24 ohms
B (Red) to C (Wht) 24 ohms
A, B or C to solenoid case 0 ohms
Results:
If continuity is not correct, replace fuel shutoff solenoid.