"Seams first" - just our logic, but not everybody may agree. We remove out all the old, cruddy sealer with popsicle sticks & mineral spirits, then polish the seams, clean them really well - again with popsicle sticks & mineral spirits, then reseal them with fresh vulkem/parabond.
We've done this on both trailers and feel that it makes sense (at least to us) for a couple of reasons. If you leave the old sealer in place while polishing then reseal afterwards, the old sealer can chunk out and get imbedded in the buffs which causes undue scratching. By doing it this way, you can get the seams buffed up really well, then sealed which leaves the sealer cleaner in the end. If you seal first w/o polishing the seams - the polishing compound gets gooped up on the new sealer because we are trying to get the 55 years of oxidation off and working the area harder.
As we've worked on the trailer, we would take things off, then polish around the area before putting parts back on. This way, the hard work is done around all the details, seams, joints, drip caps, etc. and just the flat parts are left. Yes, we still will go over those areas again, but it's a touch-up, not the original cut, so the compounding isn't as big of a deal.
You do have a funny looking trailer for awhile using this method with the polished seams only, but it's definitely a conversation piece! Looks like orange segments ~