Pull chain on the ceiling fan light broke off, so I pulled it down, and figured out what to buy, but at some point one of the two black wires going to it came loose, presumably out of a screw cap. Does it just go in the cap with the other black load wires (3 still together)? Do I understand correctly that the light pull chain just interrupts the power with an on/off switch?

I guess yes. There should be a feed wire coming in along with a white neutral. May be another pair of wires going out to feed something else on the circuit. If the light has different sections, the second switch wire will go to all the loads. I hate it when something disassembles itself when I am not looking.

Yeah, kind of scary when you pull it down and take a look, and one of the hot wires comes out. There are 6 white neutrals in one cap (this is a Hunter fan with a Zing Ear 2 way switch that broke) and then a bunch of colored wires for the fan speeds I guess. All of it connects to this molex(sp?) multi connector including the 2 way. I just needed to make sure that black is black I guess. PS I see how often you post on here- you're a saint!

Black is black. The hot goes into the light assembly from the fan's light wire (in Hunters it's usually black with a white stripe) and goes to one side of the switch. It goes out the other side of the switch and connects to the black leads from each lamp socket. All the neutrals from the light sockets connect to the neutral/white wire from the fan supply.

I have repaired thousands of ceiling fan motors. Most use three power leads, black - motor hot, blue - light kit hot, and white - netural shared by the
Motor and light kit. Hunter is the exception, they use a black with white tracer for the light kit hot. As far as the fan pull chain switch, I have seen
Hundreds of different makes but what really matters is the internal connections the switch makes. Many times if the chain had pulled out of the switch,
I would have to break the switch open to determine how it connected.

Makpruitt, CeilingFanParts.com Home has a helpful resource for pullchains.

So do I at:

Ceiling fan pullchain replacement and repair - Ceiling Fans N More