I installed a new relay and got the same results. There are 2 sources of 12 volts at the relay base.
While you’re deciding whether to get a new ignition switch, buy one of these:
As a stop-gap, you can wire 12V through this momentary switch to power the starter solenoid, bypassing the ignition switch and relay. Run the wire inside the cabin to this switch and mount it where it’s safe and easy to reach. If you’re not comfortable with elementary auto wiring, find someone who is.
Looking at some data it shows that terminal 5 should have power on it but the black wire on terminal 2 (the relay coil lead) comes from the ignition switch and should only have power on that pin when in the START position. Check the ignition switch. Disconnect it and see if the power to that pin goes away. If it does then it appears the switch has a problem internally. The drawing shows the wire for the START position on the switch is blk/wht and changes to black after the safety switch. Power input to the ignition switch is on the white wire.