Thank you for mentioning the RNC oath of fealty, I wasn’t familiar with that so I looked it up and it requires the candidate to back whomever the party’s eventual nominee is (including if it’s Trump). Since he hasn’t agreed to back anyone but himself, it makes sense why he wouldn’t want to sign it.

It also makes sense why each of the candidates in OP’s photo raised their hands in support of Trump if he was the candidate, technically they already pledged the exact same thing.