Somebody who is willing to leave the ego out, can go hard but is also controlled. Doesn't force submissions. Doesn't mind scaling down to match lower rank or fitness/strength level. Stays after practice to goof around. Somebody who you can start pummeling with when you meet on the streets.

If I needed a training partner just for me, no scaling down needed. I don't mind getting smashed. :D

Congrats on the brown!

Building on Coachpotato’s comment, I also appreciate when my partners have different skill sets from me. It sort of hurts to get beaten but the the longer term growth is worth it. If they have the attributes mentioned above, then your partner can push you in productive ways that help both of you grow

One that realizes that adults rolling around the floor is inherently silly, and therefore doesn't take him/herself and the whole ordeal that seriously.

Also, must be able to both withstand and put the presh.

Don't be a jerk. Don't use positions that might hurt, understand if your partner knows it and know what they need to do to defend before you fully lock it (for example: heel hook and the guys defend rolling to the wrong way).
Don't use full strength as it is not competition, move and create awareness. If it is a competition class, go full speed, don't go soft in a comp class. For me this is the worst, e.g. taping for shit cardio is not my problem, is yours. So, know yourself and provide a good training session to your partner.

Kind of depends. If we're doing static drilling, I want someone who is willing to work with me and not block my technique to show how manly they are. If I'm rolling, someone who respects the tap.
But mainly, someone who understands they needs to shit the hell up. I've had training partners who want to play sensei spend so much time "explaining" or trying to show me how smart they are the technique to me that I didn't actually get the chance to drill it. I even had a white belt once try to correct my butterfly guard because, "in MMA I'd get punched in the face". I then pointed out to him that I neither train nor have any interest in MMA and was told I will when I get older. Bear in mind, this guy was in his early 20's and I was literally almost twice his age.

For me anyone with a pulse can help me train jiu jitsu. Even a knucklehead eventually gets it unless I reciprocate said knucklehead behaviour.

Assuming that every sparring partner can teach you something; I think the best is the one that always puts you in trouble, working on your weak points, in order to make you improve.

Good point. I need to roll with spazzes occasionally. They give a unique energy that goes away as their training progresses

An interesting, if difficult, question. I agree with much of the above replies. To narrow it down to one quality . . . For me, I want a training partner who is willing to constantly explore rolling possibilities. There’s nothing more boring than a partner who always resorts to the same game plan. I’m not into Groundhog Day Jiu-Jitsu.

Initial attempt at making trends from the responses, plus some of my own

What makes a perfect training partner?

1 Skilled
2 Depth of Knowledge
3 Controlled Submissions
4 Controlled Movements
5 Controlled Ego
6 Modular Intensity (Flow ok, Smesh ok too)
7 Ability to give a "look", work on weaknesses
8 Friendly, playful, motivating
9 R&D mindset, discover & troubleshoot
10 Not overtalking/over explaining

bonus : good hygiene ^^, trimmed nails, fresh gi, etc.