There is no starter relay in the car as standard but one could have been added though it's not likely.
Adding one is very easy and takes a huge load off the ignition switch. I added one to my Coupe and it helps. At the same time I added a remote starter switch to the engine compartment which can come in handy.
I had your issue last year and believe it or not it was the positive clamp onto the battery that was the problem. On my car the clamp is as old as the car and as a result has been on and off a battery hundreds of times. This had deformed lead over time and even though it was clamping to the post, I believe it was clamping to a very small part of the total surface area of the post. This smaller surface area would sometimes provide enough electron transfer and other times not.
I loosened the clamp bolt and pried the clamp open, made sure the arms were level and that the interior faces were smooth. Clamped it back on, noted it sat much further down and had a more even relationship to the post and have not had the click and dim lights of not enough power on the dash since. Sometimes it's the little things that need attention... :whistle: