You don't have a starter relay and a solenoid. They are the same thing. You probably have a bad/weak battery. When it does that, jump it and see what happens. There are TWO models in 1955. 55.1 and 55.2. Which one do you have?
The starter is not supposed to spin until it engages the flywheel. So it's working correctly.
Don't mix your guess in with symptoms. Report your result after jumping. Then we can move forward with next test. Be sure you jump it with a good battery and check your battery posts and cable clamps. Take off and clean really good. Check cable and wires to starter. Check carefully.
Tell us anything you have done electrically lately with wires, battery, cables, solenoid, ignition switch...........
Don't remove starter or solenoid. That's later. Use a volt meter on battery. Touch only the posts and read. Then touch only the clamps and read. looking for 12.6V.
The only relay you have is a horn relay which also acts as a hot terminal block, sometimes, and may look like it's energizing starter.
Fords have actual starter relays.
Generally: a relay has no external mechanical linkage and a solenoid does. Their electrics operate basically the same. So confusion results.