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Hi - I hope someone can help me with this. 1980 TR7, all stock with Stromberg carbs. Canadian car.
Sometimes when I try to restart it, the electrical comes on, the lights work etc but when I switch on the starter, I hear a click and then everything goes dead. No lights, no gauges or anything.
I disconnect the battery for about 5 seconds, reconnect it and everything is fine, the engine starts right away.
This does not happen every time but about once every few of weeks.
Could it be the starter solenoid or a relay.
It is really strange that the electrical system is totally dead and somehow resets itself when the battery is disconnected for a short time.
Any clues would be appreciated.

Sounds like a crap battery connection, pull off both terminals and give both of them and the battery terminals a bloody good clean, then do the same with the positive cable at the starter motor and the negative cable where it grounds to the body.
Next, refit the terminals and tighten them properly.
Try this 1st then get back to us.

I had that problem and I chased it down for years but it kept coming back. After going through everything in the line I eventually thought it was the 12V distribution clamp on the red wire near where it connects to the battery as you could slide it up and down on the wire and moving it would bring back the starting of the car. I pulled the thick red wire from the battery to the starter so I could put the clamp in a vise and low and behold the red wire battery clamp fell off. The clamp clamped to the red wire and although the clamp's two bolts where tight, the lead clamp had worn such that the red wire was not securely clamped. I cut back the insulation a bit, folded half the wires back, cut off the rest so effectively the red wire was now thicker so the battery clamp could now grasp it tightly when bolted to it. While I had it out also tightened the 12V distribution clamp in a vise so it didn't move on the wire. Problem gone over two years now.

Many Thanks for the guidance Cobber and FI Spyder.
I checked and cleaned both battery terminals and mine did the same as FI Spider's. The clamped positive connection was very dirty.
I cut the wire of about 3/4 inch. cleaned the copper and soldered on a proper lug. Tinned the red wire and filled the lug with hot solder and pushed them together.
It is now a bolted connection.
Funny thing too, the headlights are brighter!
Hopefully this is the solution. The only thing left is to clean the solenoid connections from underneath.
Thanks again....

Don't forget to check the main earth connections onto the body and the engine.