Sonia's Driver

I'd like to get your opinions on a problem that I've been experiencing.

The engine is a D15B7.

When it is cold, there is a very long delay between when the key is turned to START, and when the engine starts to crank. When it is ~50, the delay is only a couple of seconds. When it is colder, the delay is much longer. There is no click, or any response from the engine whatsoever. After the delay, the engine cranks, starts, and runs normally. The battery is about 1 year old. This symptom was first noticed at the end of last winter, but was ignored due to other problems with more pressing needs for attention. Obviously the symptom is not very noticeable during the summer.

Has anyone else encountered this symptom? Did the symptoms get worse over time? I'm worried that there will come a time when the delay will be forever.

Does the starter relay normally/always make an audible click when energized?

My instinct tells me that it's the relay and not the starter. That said, if the troubleshooting indicates that the starter is the culprit, rather than the relay, can I rebuild the starter myself?

My working assumption is that the relay is binding for some reason, and that the low current side heats up slowly until it unbinds and is able to move the solenoid and energize the starter. How does that sound to you?

Thanks in advance for your help.