I have 2 questions about my 91 Civic DX:
1 - It has 2 lockup solenoids, what is the extra one for?
2 - How can I confirm that the solenoids are doing their thing
at the right time?

1: Are you sure it's a '91? '92+ Civics have two or more solenoids but '88-91 models (with the exception of the automatic AWD wagon) should only have one. Before your train of thought runs off down that path, it's fairly difficult to swap a '92+ transmission into an '88-91 Civic due to significant changes in engine/transmission mounting points. I guess some non-US market '88-91 transmission may have gotten two solenoids - there is certainly a space machined on my old '91 trans case for a second solenoid valve.
To answer your question, the second solenoid allows for a few stages of 'partial lockup'. I'm not sure what value those partial stages have... smoother shifting or more efficient torque transmission under certain conditions perhaps?

2: To actually check if the valves are doing what they should, you would need to purchase an automatic transmission pressure gauge set and connect it to the proper service ports on the transmission. Other than that, you can do electrical tests. A factory service manual for whatever car the transmission came from should describe the on/off patterns for various operating conditions. If there is a significant electrical problem such as a burnt out or shorted out solenoid coil or similarly damaged wire, the ECU should throw a diagnostic code.

BTW if you don't think the lockup is working, it's quite often a vehicle speed sensor problem, the ECU doesn't know it's going fast enough to signal lockup.

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There is a crude way to check them. Unplug each one and go for a test drive to see how/if the trans acts differently.

I might try that. My car seems to run pretty good. I consistently get between 34 and 36 mpg, and want to improve that, if possible. It is all stock, and I want to be sure that everything works the way it should.

It is definitely a 1991 model and has DPFI. But it also has color-matched side molding, mirrors and bumper, like the Si. Maybe late in the model year, just before the 92's came out, they added the second solenoid. Am I right in assuming that 12v is applied to the solenoid to lock it up? (no voltage, no lockup).

Is it a 2-door (CRX), 3-door (hatchback), 4-door (sedan) or 5-door (wagon)? The month of manufacture should be on the door frame VIN sticker, along with the gross vehicle weight ratings and such. My CRX was built in June '91, and it only had one solenoid. Have I been correct in assuming you're in the US?

That's the case with single-solenoid designs, yes.

Thanx for responding.
Its a 3-door HB, built in July 1991, and I'm in California.

Ah, that could be the key bit of info.
I'm not sure what tweaks the Cali-emissions models got since I don't have a Civic-specific '91 service manual... Maybe someone who does could chime in?