Don't know much about this kind of trouble but my bike did something similar for a while too, sometimes it would start sometimes not ,bad fuse. Then I ended up finding a major short which caused a bunch of blown fuses.
It might not be your problem but I guess it can't do any harm to check the fuses.

I'm sorry I am just as dumbfounded as you are then  

1 st what are you checking voltage with ?  battery charger?  on the 87 wiring diagram from the ssm there is an unfused wire from the pos of the battery(no color given assume red)to the starter relay(# 10 awg or larger ?)from the relay to the starter with a paralell y/b going to(via a plug in connector) the left most connection of the solenoide controller..other side of starter is ground would assume same gauge as red from battery(this may be loose and causing your headache)
from left to right (in diagram)at the controller colors are:
y/b,b/r,r/w,y/g,b/w.. 2 other wires at starter relay:
via plug connector y/b,b/w...
hope this helps i do have a scanner and can try to e mail diagram but wont be back from up mountain till friday...

I could be wrong,but I think it bolts on the rear fender behind the air box.And the solenoid controller is under the tank.

I checked voltage with a volt meter and supplied power via a battery charger set at 12v since I don't have a spare battery to use other than what is on the bike.

Ok folks, according to the Clymer manual, what's under the gas tank is the decompression selenoid.  What's under the seat, Clymer calls the starter selenoid.  According to the wiring diagram, however, the starter selenoid and the starter relay are two seperate units.  I believe the starter selenoid and starter relay are one in the same since it has four wire connections to it.

I believe that my problem is either the second stage of the timer control unit doesn't work every time (it was just chance when I checked it that it worked, but puts out less voltage), the second starter selenoid/relay I put in is also bad, or I simply have a bad wire/contact  somewhere between the timer control and the starter.  I hope it is not the starter selenoid because it was a %$&*# to replace.  Not much room.  Had to drop the rear fender to get to the mounting bolts.

I got on here hoping that someone has had the same problem and was able to remedy it.  I hoped that this was a common problem to be truthful.

I've been driving my B-i-L's 88 while waiting for a part for my 96. It seems to start differently than mine. I know his battery is marginal and that may be the biggest part of the problem. However I feel the source may be in the crank switch contacts -the button you push to start if you will. In any series circuit, high resistance in any one point causes voltage problems up and down the circuit. If the contacts are pitted, or corroded or both then they decrease the voltage available to operate the starter controls,  compression release solenoid and starter relay.  (FWIW magnetic switches = relays and solenoids are similar, however solenoids usually involve the moving plunger doing more than just making an electrical contact. in our case the solenoid plunger pulls up on the lever to lift the exhaust valve part way off its seat lowering the compression so the engine will spin up quicker. The relay just completes the circuit from the battery + to the starter motor terminal w/o all those amps going through the little switch) Might be worth taking apart the switch on the handle bar and clean and polish the contacts.  Max

Welll Awwright!