It sounds like a hydraulic lifter is bleeding own over time and takes a bit of time to pump back up upon startup.
+1 That is with 99% certainty what it is on this engine.
OP This causes no damage long or short term, on some engines its totally normal, probably just a little varnish in them. You could try running a 16oz bottle of Rislone high mileage the next oil change for a full OCI, if it makes it better fine if not forget it.
With an engine this age I would be a little cautious with strong solvent type additives, the Rislone HM seems to do a pretty decent job for a few bucks from Walmart.
I have some seals of different type materials including some old school neoprene ones sitting in it for the last 3 months with nothing to report, no change in size or suppleness.