How do you determine what threads something has?

I’m wondering what method everyone uses to determine the threads on consumer products they want to modify, especially injection molded products.
I’ve spent some time around a machine shop and worked in the quality control metrology department of two different companies for a number of years, so I’m familiar with thread gauges and such, but in those situations I had access to a truly shocking number of male and female thread gages in virtually every possible size, pitch, and tolerance (2B, 3B, etc.). At home, I have enough fasteners of known size lying around I can determine what size most things are pretty easily, but when dealing with… like, plastic bottles or, in this case, the molded plastic threads on a solar powered lamp, I don’t have much to go on.

My original plan was to measure the major diameter of the male threads (around 13.5mm) and the pitch (2mm) and just hunt around in Fusion 360 until I found something that matched, but I came up empty.

How do you guys do this? There are SO MANY thread standards, how do you tackle something that’s just weird and unknown?

I will either measure the OD with my digital caliber and use that to best guess if its metric or sae, fine thread pitch or coarse and compare that to mcmaster bolt drawings. All their parts have detailed drawings and measurements to compare to.
screws | McMaster-Carr

Or I use one of my thread gauge sets(thread checker set). Much easier this way if you have one.
Here’s the one I use most. You can screw a bolt/screw into the female threads or use the male threads to go into a nut/etc.

https://amzn.to/4ef4QEq

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Lots of plastic/injection moulded stuff uses custom threads. For me it is trial and error. There are few shapes in solidworks I start with and then use the profiles to print custom gages to check the shape of the profile. Then I test print full length of the thread to get the pitch right. Kind of go/ no go gauge. Hate this stuff.

Some info here but there are plenty of other resources
Screw Bottle And Screw Cap Design — China Customized Perfume Bottles Caps Boxes | iPerfume Packaging

Most likely what you need is a 14mm X 2.0 thread. Most bolts measure undersized from their nominal diameter. When I measure a thread I round up to an even size if that makes sense.

Calipers and a thread pitch gauge are what I use 99.9% of the time. Knowing where the item was made is also a leading clue, made in USA then it’s likely to be an imperial thread. Anything else is most likely metric. A thread pitch gauge will confirm this as well.