There are tests that can be run to show an immune response.
One thing I’ve learned is it’s extremely hard to get doctors to run the tests. AND there are a whole lot of them. AND I’ve run into many doctors that are 10-20 years out of date with treatment and diagnosis protocols.
As in, current recommendations are that test X isn’t reliable. Use test Y. Doctor refuses to run any test because you’re the wrong gender. AND The moment you see someone in a practice your banned from seeing anyone else in the practice. So second opinion means going to 20 miles to another center.
Oh, and it’s 3 months+ to get a single appointment. You may need two dozen appointments until they narrow in on the issue.
That something is possible still leaves a massive gap of getting it done.
Glass half empty: We don't know how the immune response measured relates to protection from or lessening of the infection. This is what the ongoing trial is trying to find out.
This is, IIRC, the second report of successful immunogenicity in older people. There was a (small) cohort of > 65 year old people tested with Pfizer / BioNTech's vaccine in the Phase 1 trial, and even there immune responses were found and measured.