2000 Camaro, both turn signals won't work, flasher replaced??

I have a 2000 Camaro. The other night I left my Dad's after dinner and
noticed immediately after starting the car that the automatic lights would not
turn on when the parking brake was released, and NEITHER of the turn
signals would work. Hazards work fine. I replaced the turn signal flasher unit,
but this did not correct the issue. Headlights work when manually turned on
with the switch. It could be that the steering column switch for the turn
signals is shot, along with the automatic light switch associated with the
brake release lever, as dual but independent failures. (I am not looking
forward to replacing the switch in the steering column, especially if that's not
the issue) I noticed that the turn signals behaved strangely at one point a few
weeks ago as if a bulb was burnt out with them not flashing and staying on,
but then performed as normal.
Has anyone observed related problems with both turn signals and automatic
light switch?
Could there be a communal ground problem? If so, where would I look for
that? Are lights grounded through their housings or otherwise?
The vehicle has several other electronic issues with dummy lights, security
light always on, low oil on when oil level is fine, and periodic check engine,
likely related to O2 sensors (already replaced) but do not affect performance
noticeably. Cruise control has not functioned via the turn signal lever for
several years. Thanks in advance!!!