Time dilation for a moving electronic clock

Note that the clock slows down as viewed from someone else's reference frame.

In the rocket: clocks, melting ice, human biology, time, and whatever else you can think of all proceed normally. (Same with length contraction: right now we are both pancake flat in the reference frame of a cosmic ray, but we don't really notice it--at all).

Of course life on Earth proceeds normally too, even though the rocket's occupants see Earth's time ticking slowly (not to mention an, ahem, flat Earth).

I recommend Feynmann's chapter on this. It is included in Six easy pieces I think. He points out that once you've found the effect for one type of clock (e.g. light pulse clock) then you have found it for all types, because otherwise the different types of clock would get out of step with one another when observed by one observer but stay in step when observed by another. That would be a direct impossibility. For example if one observer says that two clocks go "bong" at the same moment at the same place, then all observers must agree that the bongs happened at the same moment at the same place.

You can put your electronic clock next to a light pulse clock, both in the same state of overall motion, and then whenever they tick at the same moment in their joint rest frame, that is one joint 'bong'.

This is also discussed in other introductory texts of course.

All (properly functioning) clocks must experience the same time dilation, no matter what mechanism they use to tell time. Otherwise, you could use 2 different clocks to determine your absolute speed, but relativity says that absolute speed isn't a thing.