If you have a turn signal on that side, and a park lamp, the bulb and socket are good.
Turn signal/hazard/stop, all use the same filament on the bulb.
Your problem is I would say up at the dash area, as the same wire is used on all of those circuits to light the bulb, it is split off to each switch, so that each, along with the flashers can control the bulb.
If they all worked previously, and I had the old switch, I'd put it back in. If the light starts working, I'd be taking the new switch back for a replacement.
97 Sahara, 74 Renegade, 72 CJ5, 55 Willy's (the Beast) Boss 302, 6:34 gearing, Bose 901 speakers.
God I miss that Jeep. Forgot the kinda Jeep, 80 SX4.