Moving all my files to Printables for simplicity. Check out the project there:
https://www.printables.com/model/233472-f-16-sidestick-grip

UPDATE July 2023
I have uploaded this to printables.com because it's honestly just a better website than Thingiverse.

A few brief observations on the experiences of others and improvements I might try and make at some point in the future:

The trigger mech is kinda finicky. Dependent on spring force and switch actuation force. Also has a bit of a bump to push through for the second stage.
The screws are just M3 (or something around that size) direct into plastic, so not the best durability. In v2 I would probably try and add captive nuts or similar.
The wiring, well, I actually haven't wired it, but that's because it is rather intimidating lol. I really like what Bacon8tor did with his remix here and might try to build off of his custom PCBs in future versions, making the whole setup a little more plug and play, fewer loose wires, etc. I also do really like the custom hat switches though, so we'll see.

UPDATE March 2022
RJSimTech has started selling a kit version of this grip modified to work with the popular T1600 joystick! RJSimTech has been around for a while making trackir-compatible IR head trackers and when they reached out about selling a version of this grip, I was super stoked!
Check it out here: https://rjsimtech.com?bg_ref=Hbkxr6ODmH
(Disclaimer: I do get a percent of sales from that link and from sales of the grip. Also use coupon code JFlyer for 5% off if you do decide to make a purchase)

UPDATE July 16 2021
Removed printed threads from M3 holes in the left handed step files. Also included the left handed Solidworks file

UPDATE May 8 2021
I have removed the 3D printed threads from the M3 holes as some people had trouble printing them. They are now just 2.65mm holes which you can drive an M3 or similar screw into. Should be functionally equivalent; you probably won't notice a difference.
I also consolidated all source files (solidworks and step) into a single zip file to simplify that for everyone who wants to mess around with those.

UPDATE Feb 8 2021
I have added a zip file containing a mirrored step file of the grip as well as mirrored stls of the main parts. The trigger, hats, and buttons should all be the same as the standard grip so I didn't mirror those.

Hello friends! This is a 3D printable F-16 (or A-10) grip, modelled by yours truly from a blender file and a bunch of reference photos of a Thrustmaster Warthog that a nice fella from the DIYHotas subreddit gave me (check out his designs on thingiverse here). I don't own a real F-16 SSC or a Warthog or Cougar so I can't speak as to how close this model really is, but I think it feels and looks about right.

I did not design this grip to attach to any specific joystick base. I left a 25mm hole on the base with a slot cut into the front and back and figured this might make it easy for people to make their own adapters for gimbals, extensions, whatever. Feel free to design directly into the grip if you wish. (also, would adding a screw hole down there for mounting be useful?)

I modeled this in two stages, first doing the external geometry and then slicing that up and clearing space for internals. I included two step files, one of the external stick geometry and another of the trigger.

My next project is going to be the F-16 TQS as I've already got a decent start on it. I began with hempstick's excellent shell model and going from there I've been adding electronics and a base. After that's done, who knows? I think perhaps an F-18 stick/throttle will be in order but I'm open to suggestions. I'm on the HOTAS Discord as Spock. If you think this model is worth it feel free to leave a tip, and of course let me know if you have any problems with this design and I'll do my best to fix and improve.

PRINTING
I printed the main left/right sides and the top face down with supports. I've included a zip file with Prusaslicer project files if you'd like to see where I added support blocking, etc. Most parts should be fairly self explanatory.

COMPONENTS
1x Left, Right, Top, Face Plate, Nubbin, Paddle, Trigger, DMS, TMS, CMS, Trim, Pickle, Pinkie, NWS, tact switch cover
4x hatswitch base, hatswitch cap, hatswitch stem (same as https://www.thingiverse.com/thing:4543158)

4x 5-10 mm M3 bolts (3 for securing Top, 1 for paddle)
2x 20-22 mm M3 bolts
8x screws/bolts for attaching hat switches (M2 x 10-12mm)
2x screws/bolts for attaching paddle (M2 x 10-12mm)

Trigger spring (mine is 12mm long, 5mm OD, 4mm ID)

22-25x 4.3x6x6 mm tact switches

OPTIONAL:
Paddle spring (>5mm ID, compressible to ~2mm)
Secondary trigger spring

1-3x hatswitch push (you can add a push button to the CMS, TMS, and Trim hats if desired)

ASSEMBLY
The most finicky part of this design is the trigger. I've included a picture of the mechanism. Basically, place the tact switch cover over the 5mm tact switch, then the spring over that. If it's all good, you'll get the first stage click about halfway and it'll unlick when you release. If it won't release make sure the trigger moves quite freely all along the way. You may want to add a second spring (which I left room for above the first) to ensure the trigger always returns to the fully not-pressed state.

I think everything else is fairly self-explanatory. A lot of the tact switches for the various buttons need to have two of the prongs snipped off, and it's likely you'll need to cut a little material away on the NWS button hole in the right half to give enough space for the button. (and while we're on the subject, the NWS, Pickle, and Pinkie buttons are all slightly different lengths... I may fix that in the future but it's a bit too much math for me at the moment. Pinkie is the shortest and the wide part on the Pickle is thinner than the other two)

Oh, and the lower nubbin holds the tact switch for the pinkie button. The lower screw goes directly through it and into the right shell.