When it’s reasonably close to a functioning gene (coding DNA), such random/pseudo-random sequences always have the potential to mutate into a sequence that some transcription factor recognizes.

Any “Junk DNA” between a transcription recognition sequence and the promoter sequence can change its length, with potential impact on the transcription rates relative to transcription factor concentrations.

A large proportion of “Junk DNA” improves the chance that a random insertion of some sequence (such as a new copy of a functioning gene) will land safely, without disrupting any existing gene/control system.

“Pseudogene” is probably as good a term as any for a copy of the coding sequence(s) without the associated promoter and other control sequences. (Of course it would also apply to a copy of both in which the control sequences had mutated to turn them off.)

We should remember that the DNA repair system uses an available copy of a similar sequence to repair breaks: if a break in an active sequence is repaired using a “Pseudogene“, the accumulated mutations could be added to the active sequence in a package. This, in addition to the re-activation of a “dead” pseudogene, has the potential to “jump over” poor fitness landscapes of individual mutations to land on a beneficial package of such mutations. Of the two processes above, I suspect the first is much more common.

Which then come back to life. Or resurrected.

I henceforth name these genes “Jesus Genes!”

(I was going to go for “Zombie Genes”, but I liked the alliteration.)