The glow plug relay - what you are probably calling the solenoid - is what does the work. The controller tells the relay when to do the work.
Bypassing the controller is easy but you will need to run a button in the cab to do what is called 'manual control'.
The relay has two big posts and two little posts:
One of the big posts should have two fat wires coming from hot- usually tied in from starter relay. Either yellow or brown, I don't remember sorry.
The other big post is usually hooked up to a flat piece of metal with zigzags - this runs to the glowplugs. You can leave it be.
The two small posts - one is for the "signal" to turn on, the other is to ground the relay.
Unhook any other wires that I didn't describe, these are the controllers' and we don't want them.
There are two ways to make it so YOU are in CONTROL.
The easy way - get a piece of wire maybe 3 inches long, strip both ends. Find a large ring terminal that fits onto the large post that is hooked up to constant power (not the metal zigzag thing, it gets temporary power). Crimp that terminal onto the little wire. Find a ring terminal that fits on the small posts, crimp it onto the other end of the wire. Now attach the little end to the little Signal post, and the big end to the hot big post (not metal zigzag piece). Then all you do is run a wire from the small ground post into the cab, hook it up to a push button switch, and run another wire from the switch to anywhere in the cab that is grounded (which is pretty much anything that is metal - tons of stuff under the dash
).
The slightly harder way is to run a wire from ground to the small ground terminal, and then run two wires into the cab for a push button switch. One wire from the small signal post on the relay to the button, the other from any 12V source to the button. Doing this also increases risk of shorting, because if either of these wires get rubbed through they will short to any ground whereas the 'easier' method IS a ground already (but would cause the relay to come on, still better than burning down your truck..)
Otherwise everyone else will tell you to fix the controller system.
Good luck, there are tons of pictures and info online about how to do "manual glowplug for idi"s on google.
HERE at the bottom of the picture is what I was trying to describe as the easy method, but taking off the controller wiring
http://www.dieselhub.com/maintenance/maintpics/gp-controller/manual-glow-plug-switch.jpg
Here is one i found on google, but the picture shows the slightly harder way of doing it
http://www.ford-trucks.com/forums/1222586-new-1992-f250-runs-great-wont-start.html#post12820923
didnt read this one, picture at bottom looks a little odd
http://www.oilburners.net/articles/glowplugbypass.htm