The Mystic LED manual doesn't discuss the pass-thru connectivity. Odd, it should at least mention it in passing. The web site does mention it.
The Quad Gem LED doesn't mention a power pass-thrue in the manual or the web page, at least from my quick examination.
IF the connectors are identical for pass-thru and input(as in they match such as IEC, Edison, whatever), it really shouldn't be any big deal. When we look at it, an Edison cable is electrically compatible with an IEC cable, it just needs the proper end placed in the proper location. You'll also note that your IEC cable that goes to your computer and perhaps some of your other equipment starts with an Edison connector attaching to power with the angled IEC connector at the other end. Making the cables yourself would be a bit annoying as I can't just find IEC connectors, I end up having to go with pre-made cables.
In regards to your question about chaining the Mystic LED to your Quad Gem LED, I see no reason to NOT do it. If the Mystic has an IEC pass-thru, you may have a bit of a hassle getting a proper cable for it. These aren't rare, but they aren't super common while at the same time, they aren't difficult to obtain. I know of a place where if I wanted, I could pick up a dozen of them any time.
The bigger issue is ADJ. Most of their fixtures, to the best of my knowledge, are hard-wired with a power cable, which I sort of don't like. I would prefer detachable IEC cables. Why? My Mystic cable broke and it was a royal pain in the butt to replace. I had to take a spare IEC cable I had laying around and lop and end off and then strip it back a bit and strip ends to resolve my issue. Works great, but I hate sacrificing cables like that.
Your issue would most likely be that the IEC pass-thrue cable(with the pins in it and a surrounding sleeve protecting the pins would then terminate in the typical IEC female connector you're used to seeing at the back of computer power supplies and monitors and lots of other fun gear.
What I would suggest is some cable sacrifice. This is ALSO safe! Get yourself that IEC pass-thru cable and chop off the female end. Get yourself to a hardware store and get yourself a decent Edison female connector that uses screw-down connections and has a strain relief of some sorts. These connectors can be readily found at most hardware stores(Lowes, Home Depot, Ace, OSH come to mind in case you need direction) or many electronics stores. They aren't terribly expensive and tend ot be pretty rugged and reliable. You'll simply want to match the colors as shown on the little paper insert or find a charge on the internet and make sure you pin it out and test it it with a meter and/or outlet testor before you put it into service.
Another note about these connectors: All you need is a decent sided phillips head screwdriver, and chances are you've got one of those already. You don't need to do any soldering. You should also have a tool or something sharp to facilitate not only the cable cutting but stripping of the individual conductors. Chances are you've got a wire cutter already, so you're probably all set as far as that is concerned. You probably won't need to strip more than a fifth to a quarter of an inch off the individual conductors, but may have to strip up to an inch of the outer jacket to facilitate moving the conductors into position. No soldering is required and in this situation, I'd recommend against it. Just twist the exposed conductor wires into a tighter wire(per conductor, not all into one) twist and then insert into the appropriate post. Good metal on metal connection is what you're after.
Go have fun. If you take more than 15 minutes doing this, then you're probably distracted.
Remember, you should have:
Wire cutters, preferably with some stripper functions. Shouldn't cost more than $8 for this.
Meter with ohms and/or tone for measuring and testing connectivity. Go cheap unless you think you'll use this a lot, in which case, don't go nuts, they can get super expensive fast. You can get a suitable one for under $15 or less. You just need a basic one. Radio Shack can be our pal here.
3-prong outlet tester. These can go anywhere from $7 to $20 depending on brand and what other features you want(like GFCI testing). Radio Shack makes a decent one wiht GFCI testing that was I think around $8
Phillips head screwdriver. Don't go nuts on it, but any decent handheld with a #1 head will be sufficient. Unless you need a super durable one, you can spend less than $5 and get a decent durable one on special.
The replacement connector: Less than $5 for a good one I bet. I usually have to buy male ends because a certain someone likes ot whack grounding pins off of them.
Remember, this is SAFE. That's very important. I know there is going to be some excess cable, bt that's a good thing. And if you aren't long enough, now you can add in your own extension.
Enjoy. Have fun.
