Relative time vs Absolute time question

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>There are 2 lightbulbs 2 light minutes apart from each other.
>The lightbulbs are set in the beginning to turn off and on every 120 seconds (2 light minutes visually).
>Their clocks are calibrated right next to each other.
>One lightbulb is then moved 2 lightminutes away from a from the other lighbulb.
Once the lightbulbs are 2 light minutes apart, do the lightbulbs stay synchronised?
Even if the lights aren't flashing on an off at the same time visually from your perspective, if you bring them back together, would they match up again?

I'm trying to wrap my head around time dilation and relativity. Any anon help would be great.

https://www.quora.com/If-the-speed-of-light-was-multiplied-by-x2-x3-x4-etc-across-the-universe-would-the-boundaries-of-the-observable-universe-increase-by-x2-x3-x4-etc?ch=10&share=0a540b18&srid=X9X21

https://www.quora.com/If-the-Sun-is-around-8-light-minutes-away-if-the-Sun-just-turned-off-like-a-lightbulb-did-it-turn-off-as-you-saw-it-on-Earth-or-8-minutes-ago-is-time-pegged-outside-your-reference-frame-or-is-the-speed-of-light-the?ch=10&share=a75fe093&srid=X9X21

The answers from these questions might help illustrate what I'm talking about

If something is 1 light year away, if you model its movement forward in time 1 year relative to your own reference frame, isn't that where it is from a non relative perspective, or higher vantage point/dimension? As in the past is taken out of the way.