91 Civic EACV questions/diagnosis

I have been having some idling problems and decided to check out the
EACV system on my 91 Civic HB. No ECU codes, car starts fine. The main
symptom was the drop in idle speed to 500rpm when the engine was cold
and I was braking. Symptom went away after the car warmed up.
Following the troubleshooting chart in my Helm's manual, I proceeded
as follows:
1- Checked the resistance across the terminals of the EACV. Got
12ohms, within spec.
2- No continuity between each terminal and body ground - as expected.
3- Valve clicks when battery voltage is applied across the terminals.
4- Turned the ignition on, checked the voltage across the connector.
There is 12V - not expected according to the manual since the ECU
should be suppling the ground when EACV is activated. Confirmed by
disconnecting the ECU harness that indeed ECU is suppling the ground.
5- Put in another ECU - still voltage at EACV when ignition is on.
6- Put in another EACV - same problem with idle
7- New vacuum lines, bled the coolant - same problem with idle.

Question: Is it true that there shouldn't be ground supplied to the
EACV while the car is not running? The car was cold when I did these
tests so is it possible that ECU checks the coolant temperature and
decides to engage the EACV even if the car is not running?
Any ideas?