Battery is full, when I turn the ignition on and press the starter - small click sound and all electric dies. after several minutes the electric come back.
Any ideas to resolve?

 

I would start by checking battery terminals then head for your starter relay, starter solenoid and then starter motor, in that order. If you don't know what you are doing find someone that knows how to use an electrical multimeter and they will be able to track your issue down very quickly.

 

Before you attempt any troubleshooting, you must make sure the battery is fully charged and in good working condition, to do that, have it load tested.

Once you know the battery is good you can troubleshoot.

Clean all the terminals on all of the battery cables.

Do not buy a new starter...

 

There are a lot of connections that could have corroded over 37 years. It is better to start with a DVOM before opening up your wallet. Some common things to check are:

Battery cables, and their connections.
Circuit Breakers, I believe there are two on that model.
Relays
Also look up Click of Death. It's not as bad as it sounds.

There are also Shovelhead, and Evo sub forums, not sure which yours is.

https://www.hdforums.com/forum/shovelhead-62/
https://www.hdforums.com/forum/evo-classic-models-84/

 

I recently went through this same issue with a new HD battery...battery checks good, system charging normally, cranks and runs great...then won't. Went through the charging system several times without finding anything wrong before I finally got a free warranty replacement on the 6 month old battery...no problem since.

 

Hi from the UK and welcome to HDF. The small click you can hear is a thermal cutout, your bike has several of them. It functions like a fuse, except instead of blowing and needing replacement, it over-heats and cuts power to that circuit. After it cools down it resets itself, so your electrics work once more.

You need to identify which cutout it is and diagnose the fault on that circuit, so you can repair or replace accordingly. You really need the factory service manual, to help you diagnose the likely cause of your problem, or an expert on vehicle electrical systems.

 

the circuit breakers are under the speedometer/tach. there are 3 breakers under there. i would focus on the ignition circuit breaker. all 3 are 15 amp and you can get them at any auto parts store.