Hmmm. I tried it with an ohmmeter and didn't get what I expected.
Resistance increased to around 100 ohms and stayed there from around
60 dB up.

So, if I put 5VDC across one center pin and ground, I should be
reading voltages to ground at the other pin that correspond to the dB
setting on the dial?

Sure. with 1 volt in, turn to 20 dB attenuation and the voltmeter should
read 0.1 volt.
Bear in mind, the resistors in there are rated 0.5 watt, so don't go
applying 100 volts!
Most often, a damaged step attenuator will have only the first step damaged.
It sacrifices itself and protects subsequent stages.

AHA! Also, don't forget to terminate the attenuator in 50 ohms. That may
have been where you were having trouble. Essentially, the "voltmeter" needs
to present 50 ohms to the pad or things will NOT be nice.

W4ZCB