Timequest is also known as Time Quest, via the printed disk label and the opening title screen, and the title is given on a followup screen as Timequest Adventure. I’m honestly beyond being surprised when this sort of thing happens, although no game can match the pure naming chaos that was Dragon Quest Adventure. Perhaps unsurprisingly, Timequest shares a publisher in common: The Programmer’s Guild.

From the Museum of Computer Adventure Games.
The author of Timequest, William Demas, is better-known for doing the majority of work on Scott Adams Adventure #12 (it was a scenario like Pyramid of Doom where Adams just did some editing) and two “talking games” (Forbidden Planet and Forbidden City) for the TRS-80 published by Fantastic Software.
Timequest, on the other hand, has fallen down a memory hole of sorts; CASA is light on information, Mobygames has wrong information, and its existence doesn’t get mentioned at all in this interview with the author. There are no hints or a walkthrough anywhere, and nobody I can find has played it on video.
This is nearly identical to Journey Through Time in the premise: go through time, nab treasures, 12 in this case. However, the time periods don’t really have any theming; it’s more like you’re using a general teleportation device rather than visiting Nero or printing yourself a brand-new Gutenburg Bible.
Rather unusually, the game does not start with “home base” in the “present” of 1981.
Yes, 1886. I suppose a time traveler’s home base can be any-time and any-where. You can PUSH LEVER to go to 2930 or PULL LEVER to go to 1235. There are no other time periods (at least as far as I’ve gotten).
The “where” is somewhat important, though — there is some sense that you are fixed in location as you travel in time. The machine starts in a basement, but you can drag it outside (PULL MACHINE). If you travel forward in time while outside, you end up outside a mountain.
If you travel forward in time while inside, you end up inside the (fortunately hollow) mountain.
Traveling to the past while the machine is outside is fatal; your machine falls into a swamp. If the machine is in the basement, you get taken next to the swamp instead.
So (as of yet?) there are two 2930 locations, one 1886 location and one 1235 location.

My map so far, but certainly not complete, given I’ve only seen 3 treasures out of 12.
Even though the game doesn’t fully use the “fun” aspects of time travel (historical events and/or setting up paradoxes) the map still gets naturally broken up in sectors, which gives it a crisp and modern feel.
Besides figuring out the time machine itself, the puzzles so far have been straightforward; I found a key in a sandbox and used it to unlock a room that is supposed to hold treasures. The same room had a snorkel which I used to get a fish and gold trident from a river; I also found a flashlight lying around which led me to get a gold chain and shovel. The shovel then let me dig to an underground area in 2930.
I’m stuck on
1.) the underground area, which has a reel of tape, some silver coins, and an angry mole; while I can get in, the angry mole kills me if I try to get out.
2.) 1235 has a cave guarded by a lion.
3.) 1235 also has a swamp which you sink in and die if you try to go in (this may just be a trap)
4.) 2930 has a dead raccoon that is diseased and you die if you try to pick it up (the game implies you need gloves).
So far, I have yet to use a BRASS RING (that you start the game with), a FISH, a FROG, a FUR COAT, and some SAND. The two treasures I’ve gotten which may or may not be of use are a GOLD TRIDENT and a GOLD CHAIN. It is of course possible that the KEY, SNORKEL, and SHOVEL somehow get reused, but otherwise, that’s all I have to work with. (The snorkel doesn’t work on the swamp; you can’t kill either the mole or the lion with the trident.)
The game has me interested enough I haven’t resorted to hacking at the game file itself yet. If you want to try it out, this link will let you play online (it’ll delay, then give an error, then you need to type TYME2 and hit ENTER).

Frog is another William Demas game. This is the first I’ve ever seen an in-game ad for something sold by an entirely different publisher.