Lights come on.
Hazard lights come one.
Turn signal comes on, but doesn’t blink.
(And. . . just in case you’re wondering. . . No, I don’t:D)
light bulb out
Get a friend to check the front and back while you turn the blinkers on and off. Either front or back bulb is out
On every car I’ve ever had, when a bulb has blown the indicators blink faster than usual.
On newr cars they won’t blink if a bulb is out. Strange that neither side will not blink unless two bulbs are out. Also some cars have a seperate fuse for front and rear signals so you might also check fuses.
Apparently there’s some misunderstanding. The “lights” to which I’m referring are the lights inside the turn signal, not headlights.
IME, two bulbs often go out at the same time. (Or near enough that it seems like the same time.)
So, the bulbs are OK but the blinky part isn’t, except when in hazard mode?
On both sides?
Edited for clarity:
For both front and rear, and both sides:
Non-headlights (the red ones) light when the headlights are turned on.
Hazard lights light up and blink.
Brake lights work fine.
Turn signal comes on, but doesn’t blink.
Don’t turn signals and hazard lights use the same bulb?
My guess is the relay. At least on some cars, while the bulb is the same for hazard lights and turn signals, the current goes through a different relay. Replace the hazard light relay (cheap part) and see if that fixes it.
You mean the turn signal relay?
Right, sorry, got it backwards.
Every time I’ve seen this problem it’s been the relay. Of course “every time I’ve seen this problem” gives you a total data set of about 3 instances. 
Thanks. That’s worth a shot at trying.
I second the relay.
Is that the same thing as the flasher?
I don’t think so. The relay would be in a panel with other relays, for the horn, lights, wipers, etc. The relay isolates the higher voltage and current side from the lower voltage and current at your fingertips.
Yes, it is the same thing as the flasher.
This is usually a burned out bulb. Second cause is a blown fuse and third is a short or fourth broken circuit.
OP says “Turn signal comes on, but doesn’t blink.” Can’t be the bulb, unless this car has separate bulbs for turn signals and flashers, which would, I think, be unusual.
It’s a gutsy turn signal. You’ll have to find some other way to intimidate it.