Ok finally some warmer weather in PA. I jumped the dome light courtesy light timer and got the dome lights to work with the doors opened. It needs a new dimer timer $$$$, Thanks for all the help in that department.

It could be that the relay is stuck. Either that, or one of the pin switches for the doors or hood is grounded. The terminals on the pin switches are TINY, and they get damaged very easily, so one of them may be grounding to the switch body. also, make sure ALL of the pin switches are adjusted to where the door(or hood) will actually open the contact when the door/hood is closed.
My first guess is the relay itself....

I took the relay apart because prior to this the horn would not go off at all, I could not get it to arm or work. Cleaned the relay because it was clicking... Now no clicking but it goes off as soon as I turn the key to arm it. With it armed and going off thee 3 switches are compressed I took each one apart and cleaned and sanded the terminals, but who knows???  Each as a black/ground wire but who can follow it where its to be grounded???  I purchased the electrical trouble shooting book and lookng at this also.   Thanks for the info BB78

On my 79, the bracket for the hood switch kept bending down too far, causing the alarm to go off, Hope that helps.

Each of the wires goes back to the relay. When the switches are closed as when they would be with the doors/hood opened), they go to ground, which trips the relay on, which then closes the contact in the flasher, making the horn "beep".
I still believe the relay has stuck closed, keeping the system armed. Be VERY careful until you find/correct the problem. If the relay is stuck closed, it can overheat, and may possibly start a fire, unless the battery runs down first.
You can open the relay back up, and plug it in with the cover off, and see if the contacts are staying closed. If they are, unplug the relay, and see if the contacts open. If they do, then you definitely have a grounded switch pin wire(s) somewhere. If the contacts do NOT open when you unplug it, the relay is stuck. Be sure that the hood, and the doors are both closed while you do this.
If the relay appears to not be stuck, then remove each black wire from the pin switches one at a time, to see if the alarm goes silent. If it stays on with all three switches dis-connected, then you'll have to dig in to see which one is grounded somewhere except where it should be, which is at the switch itself. The easiest way to check that is by removing each circuit wire AT the relay itself. Whichever wire AT the relay turns the horn off is the circuit(wire) that is grounded. From there, you'll either need to trace the wire out to the pin switch, or simply run a new wire from the pin switch to the relay. I'll look at the wiring diagrams, but I'm not sure if the ones I have have the alarm system in them...
It sounds a lot harder than it really is...I hope this makes sense.

I also have push pin alarm sensors on the T Tops where the peg goes into the body when you push the lever up. Do you have these on your 78? Just another possibility...if the pin isn't going in far enough, the alarm may trigger near automatically...

Thanks again for al the info will check it all out just as soon as I can get some time.Will let you know . again thanks for the info!  BB78

From what I can tell I have an EARLY 1978 corvette without the t-top alarm pins, either that or they forgot them.  But from the wiring diagrams this  appears to be an early model so no pins! As soon as it warms up again Will get the meter out and pull the relay and test it and the wires and also checked both ground straps under the car and cleaned and replaced so have not been able to recheck the alarm since. Thanks again for the info, I will get her working one way or another. Finally got the washer bottle back into the compartment. Someone had epoxy ed the door/cover that you go up in through...Like I said I would have loved to have had this car new! How could yo do such a thing????

"BUBBA" is everywhere! Who knows why people do such stupid things to their cars!

ok for the good news, again thanks for al of your help and finally got  1 hour to fool around with the alarm.  pulled the relay and armed the door and the relay was not stuck and it was making contact and sounding the alarm, so no stuck relay but something else was making it sound. So took Joel's checklist and went through it.  NOt the driver 3 pin plug but when I was able to use  a wooden dowel in the left hand and stretch as far with my right hand to the key in door I was able to arm the door and hold down the hood switch all the way. well as Joel and some of you stated the alarm did not go off until letting go with the dowel and relaeasing the switch and presto the alarm worked....pushing bac down with the dowel and alrmed again and no alarm until releasing the switch.  I had checked this before and also marked it so I could tell the hood made contact and pushed down but  I guess not far enough and the wires I had took off to clean the contacts and the switch. It looks like I might have enough room to move the switch holder up a little not sure if enough but will elevate it to the proper height...so thanks a million...ok now the bad news..... tried to hot wire the dome light to come on as the delay timer must be bad, could not get it to work...seemed like I was to bypass and connect the orange to the pink/black...idf I read the diagram right... had tried this weeks ago just sticking wires into the connector and got the dome to come on but today no working with the wire jumped from one to the other... don't feel like shorting anything out so will bite the bullet and get a new timer$85....... seat out on my back head stuck on the steering column and the flashlight goes out????? could they have made it easier to get to the fuse box...I have sevearl dangling wires would like to get in order and feel I have some losse connections with  the radio sometimes works sometimes it does not...Has anyone pulled the fuse box out so it would be easier to get to the bat/ign/main wires and others spliced into  them redo the connections?????any help here???let me know.. Wil finish the alarm up this weekend and onto the delay timer. Thanks again 78BB