Well, I should first say that I applied in person, back when applying in person was still a thing.
To answer your specific question, I didn't include a cover letter, as I was there to explain anything if they had questions. But since my husband's post was coming to our new address, even though he was away during the week, we didn't think we would need to explain it anyway. Our post was addressed to the two of us at the same address, so that was our proof of relationship. They didn't seem to question his Salisbury work address versus our southwest Wales home address.
If you're really worried about your situation, keep the logs of your contact while apart, and explain it in a cover letter. I tend to use the term "proof of cohabitation" on this site, because that's essentially what the default evidence is. But the rules are looking for "proof of
relationship", which is why you show that you were living together when/if you were (by correspondence sent to the same address),
or you show how you maintained regular contact if you weren't living together (through chat logs, etc.). You're going to have the option of including both, so you will have plenty of evidence to support your genuine and subsisting relationship.
