Electrical – How to connect a light to box with 4 black wires, 3 white wires

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I'm trying to wire a pullchain fixture in a closet. There is no switch, that I know of, and no fixture currently. There are 3 black wires taped together and pigtailed with tape, no wirenut. There is 1 single black wire. There are also 3 white wires with a taped pigtail. How do I go about wiring a pullchain light fixture?enter image description hereenter image description here
The closet is a small coat closet next to the front door. There are three switches in the box next to the door. One is for an exterior light. The second is wired to a wall plug. The third is a question mark. An electrician replacing plugs had no idea what it was for. Perhaps it's for the fixture inside the closet?
I have a circuit tester. Can I touch black to black and red to metal box since there's no ground wire?
Ok. Just checked with black to black, red to white and flipped the switch. No light on circuit tester.

Update. There are actually 4 white wires. Three are taped together and pigtailed with no wirenut. The 4th is taped
to the pigtail. Looks like a mess. And yes, US, built in 1958.

I'm thinking I'll take the tape off and put wirenuts on. I'll update on what I find under the tape. May take a few days till I get to it. And perhaps putting in a pullchain fixture is not that important after all.

I tested the single black wire based on your recommendation.

Final update: Problem solved. I had to call our electrician for a gfci issue on on of the circuits. He also wired the pullchain fixture. I unwrapped the tape on the pigtail clippings he left behind to find that they had been crimped originally. Thank you for taking the time to answer questions!enter image description here

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Final update: Problem solved, but not by me! Had to call the electrician for a recently installed gfci issue. He wired the pullchain fixture at that time. I unwrapped the tape on the wire clippings he had left behind and found that they had been crimped. Thank you all for your responses.