I need to be able to test photocontrollers/photocells, as I want to get some for my collection.
The problem is that I have no fixtures to test with!
How can I test them to make sure they work?

I think using a 20W filament lamp as a dummy load plus alligator-wire interconnection should work. Keep the incandescent out of treach for the sensor and test it by the room light (and/or a flash light or gradually shielding it).
Some carton box may help, as some photocells feature delay in minutes or so...

And maybe some little pieces of plastic to act as insulating barriers.
But do you think typical alligator clip leads can handle the voltage?

On a tidy, wooden desk and for just that supervised test, yes.
For a permanent or other long term installation not.
Of course, you should be careful to not create any short circuit or touch them (shock,...).
Of course, count on the sparking when they do slip and short circuit - so no easy flammable things near by...

I want to also have a GFCI/GFI and fire extinguisher nearby.

I got the photocell, but what are the right connections to make? There's 3 pins/contacts.

Go through the posts here, the contact arrangements is standardized, so you should be able to find here which contact is which.

Or if you are able to easily open it, you may identify the terminals yourself:
The Load output is connected to just the switch element, so the power contact, or in case of a triac switch type one lead of the triac (and possible snubber) and nowhere else.
The line input is connected to the other terminal of the power switching element (contact or triac) and then to the control circuit (either the CdS and relay coil/heater or a lot of points in the electronic one)
And the last one, going only to the control circuit, is the Neutral.

Now if you connect another ~100W lamp in series with your lamp input (using it as a kind of fuse), even wrong connection then can not damage the photocell...

But I don't know what search words I should use.
Maybe I should get a socket and see if the wire colors tell me what connections should be made.

But I don't know what search words I should use.

Just typed "Twist lock photocell wiring diagram" into the Google and in about 3'rd or 4'th row was:
this link


But if you use the series 100W incandescent in the input wire for testing and about a 20W lamp as the load, you may just determine the connection by just dumb try-and-error. You have 6 possibilities, one of them is the correct one. If you connect it wrongly, it either does nothing at all (many electronic in any wrong connection, swapped line input and neutral), cycle/buzz (the electromechanical types, when you swap input and output) or worst case (if you connect the mains input across the contacts) the 100W lamp will light (that is, why the 100W lamp is there in the line input- if you happen to connect toe to-be-mains-input across the working contact).

There is no Ground connected to the photocell. Neutral is not Ground

Now it's getting even more confusing!

The photocell has three terminals (Neutral, Line input and Line output), I guess you just do not know which one is which on the socket (so lets mark the socket contacts as A, B, C for now). Of course, only one connection is the right one.
So if you want to connect it just random way, you have 6 possibilities:
LI-A, LO-B, N-C
LI-B, LO-C, N-A
LI-C, LO-A, N-B
LI-C, LO-B, N-A
LI-A, LO-C, N-B
LI-B, LO-A, N-C

And one of them is the correct one and so will work...

The test setup will look like:
(copy the next into e.g. a notepad or so, something with a fixed character width)
                 ___
                /   \
Line Input ----|100W |----> LI         LO <------
                \___/           Tested           |
                               photocell        ___
                                  N            /   \
                                  ^           | 20W |
                                  |            \___/
                                  |              |
Neutral Input --------------------O--------------

The "100W" incandescent just limits the current when the power contacts would be connected between LI and N, so to prevent short circuit.

I do know that the photocell has the markings for Li, LO, and N, but I didn't know what wires went to which.
Could we remember this by thinking that this is like IO on a computer?

The N is the Neutral, so you have just two possibilities to try. And one of them will work, of course if the photocell is OK...
For the first try I would assume Li as the input and Lo as output, but with that I'm not sure at all.
What I'm pretty sure is, by just swapping the Input and Output (so at least correctly identifying the Neutral) you can not damage anything...

The N is the Neutral, so you have just two possibilities to try. And one of them will work, of course if the photocell is OK...
For the first try I would assume Li as the input and Lo as output, but with that I'm not sure at all.
What I'm pretty sure is, by just swapping the Input and Output (so at least correctly identifying the Neutral) you can not damage anything...

That's the thing with AC power, you can reverse the power and devices will (usually) be just fine.