Providing you have keyless entry, Drew has probably identified the source of the 10 second (that is the spec in the ETS manual) relock. That is a standard keyless function and normally occurs when you unlock the car using the remote; but, do not open the door. Unplugging the keyless module and seeing whether the relock goes away would be the quickest way to confirm that keyless module is the source of the relock. However, the module might not be the source of the problem. The module will initiate a relock if
- the driver's door or the front hood is not opened within 10 seconds of getting an unlock signal
- the switch in the ignition switch indicates that the key is still in the ignition switch (a rather confusing feature; but, that is what the ETM says)
To prevent the accidental unlocking of the doors and
leaving them unlocked, the keyless door lock control
unit will lock the doors automatically within 10 seconds
of an unlock transmission if the driver’s door or the front
compartment are not opened (switches closed) or if
the key is placed into the ignition (key switch closed).
So, you could have a problem with the door switch, hood switch or the ignition key switch which is confusing the keyless control module with an unexpected input sequence. You need the 1992 Electrical Trouble Shooting manual to sort this out because the service manual does not cover the keyless module.
If it is a door /hood/ key switch this is something that you might want to really fix other than patch it by unplugging the keyless module. Door switches in particular can be a sign of something going sideways with the latch. I think there is an Acura TSB covering problems with the switch in the latch which can cause problems with the keyless unit.
If you don't have a keyless entry unit, there should be no re lock function. However, you have a JDM spec car and while 95% of the car is pretty much the same as a North American spec car, JDM spec cars do have very specific differences - like the catalytic converter temperature alarms so perhaps this is a uniquely JDM feature.
As a final fling, since the problem started after a battery replacement check the condition of the battery post clamps to make sure that they are clean and tight. Failing battery post clamps can cause voltage issues and erratic operation of things like the keyless when the engine is not running to establish the vehicle voltage. NSX (Honda / Acura) battery post clamps are a bit notorious for being easily damaged by over tightening - they stretch and the clamp metal actually tears.