I had little time to work on this some more today. I removed the air cleaner housing and the plate that it and the fuel filter mounts to so I could gain access to the fuse block assembly. Boy, when they put these things together they sure didn't think about what you were going to have to do to work on them. Every where it was possible they hid the bolt heads or nuts behind something to make it nearly impossible to get a wrench on them. Anyway, once the I got all of that stuff out of the way, I could see that there was about a half inch of gunk on everything. You couldn't tell what color the wires were, where they went, or what was connected to what, so I spent a chunk of the afternoon de-gunking the left side of the engine compartment. I was literally taking gobs of goo out by the handful. Then I sprayed it all down with some of that spray cleaner and wiped it out with paper towels. At least now I can see what is going on, and if there's a leak I'll be able to see where it's coming from.
Next I removed the relays and the fuse blocks from their bracket, and took the bracket out of the way so I could flip them over and look at the back side where the wires are. There are fourteen wires from the fuse blocks and they are all either red, red with a white stripe, or orange, and they all go into the wiring harness, no jumpers straight from one fuse to another. All the wires seemed tight and there was no visible corrosion. I took the clips off of the back of the fuse blocks and tugged on all of the wires to make sure they were connected, and they were. Still, I cleaned all of the connections as best I could, and I fiddled with the connector on the switched power relay some more, since it was more accessible now, to make sure it was clean and tight. During this whole process I occasionally turned the key on to check, and the circuit would sometimes work, sometimes not. The more I did the more it seemed to work, but who knows.
Since it was a little warmer today and my hands weren't numb this time, I went back and cleaned the ground and power connections that I had fiddled with or looked at before. That seemed to make a difference as well, and at the end of the day the circuit seemed to be working consistently and the BICS panel was lighting up brighter than it had before. If it's still working tomorrow, I'm going to put it all back together and try it. There wasn't really any smoking gun, I think it was just a case of several marginally dirty connections adding up to enough resistance to cause a voltage drop in the power to the relay coils, so that they would sometimes close in and sometimes not.
While I had it apart I also took the opportunity to take the relay/fuse block bracket into the garage and weld the heads of the relay mounting bolts to the back of the bracket. Now, if I ever need to replace another relay I won't have to take half the Bobcat apart to get a wrench on the bolt head.
Anyway, thanks for your help, and have a merry Christmas.