Perhaps a skilled Time Lord can consciously conceal his "psychic footprint" from others when he wants to?

In Shada, the Doctor actually lands his TARDIS inside another TARDIS and doesn't notice

The Brain of Morbius as well, although that may not count, as they use a machine to facilitate the connection

Notably, certain Bill & Ted fans at the time dubbed the phone booth time machine the "Retardis"

The funny thing about RoS was that Palpatine talked his way into defeat. He said if Rey killed him he would win, and then kept on repeating it -- effectively talking her out of it. If he'd just kept his mouth shut he would have won! #silenceisgolden

@ceejayoz Great observation. Palpatine in RoJ actively goads Luke to strike him down....

Sadly the original stories are not available in their original form (that I know of). "Flatlander" sort of hodgepodges the short stories together into a not -quite-consistent novel.

Not the one you're looking for, but this is similar in concept to Piers Anthony's "Split Infinity" trilogy In that case, it's parallel worlds that are fantasy/futuristic sci fi.

Doctor Who did this a couple years ago as well. A spacecraft near a neutron star. Each minute at one end was a long time (days/ weeks?) at the other end.

I recall a comic in which Batman comments that he wears a bright yellow oval on his chest because it's easier to armor his chest than the cowl

Not sure the DS9 “Far Beyond the Stars” characters count. Aren’t those “dream variations” of their primary characters?

Not quite the same question — positions vs. ranks

Here it is: scifi.stackexchange.com/a/99480/87750 EDIT: Hmm... maybe that's not what I saw previously. I seem to recall a longer list, but I can't be sure