Wondrous Item, uncommon
While lit, this hooded lantern burns for 6 hours on 1 pint of oil, shedding bright light in a 30-foot radius and dim light for an additional 30 feet. Invisible creatures and objects are visible as long as they are in the lantern's bright light. You can use an action to lower the hood, reducing the light to dim light in a 5-foot radius.
Notes: Detection
Would this still work if continual-flame was cast inside it on the wick?
Up to your GM I would assume. If it were at my table I'd not take issue with it, but I would make it very clear that the person holding it would always be illuminated and would likely give them disadvantage on stealth related things because of it (even if the hood of the lantern is lowered). I suppose one could throw it in a bag or something though, but that would mean making noise or taking time.
I will say, it seems rather expensive to do things that way. You burn a 2nd level spell slot and 50gp worth of materials. But if I were running your table, I wouldn't say no to the idea. I'd just try to clearly define some situations you may encounter and the cost of doing things that way.
This is way, way better than See Invisibility, which only lets the caster see the invisible creature.