Is it okay to run a 160 60 17 rear and a 120 70 17 front on a 89 gsx750f ? Also is there an integrated tail light I can put on aswell

As far as the tires go it can be done but it's not a wise idea, both because of insurance and handling purposes. Couldn't tell you about the integrated tail lights.

It isn't wise to deviate from the original tyre size specs, mainly because insurers these days are looking for reasons not to pay and unstated modifications are high on their list. Deviating from OE specs regarding tyre sizes should be reported to your insurer, in fact any modification including some cosmetic mods should be reported.

Somewhere on the proposal/policy there will be small print telling you that you must volunteer all information that might affect the premium whether there is a specific question about it or not or the policy could be void.

With motorcycle tyres the most important thing is to ensure the front and rear tyres are compatible, ie., they have similar slip angles (similar construction) or in practical terms the rear tyre should exactly follow the front.
There is little more off-putting than riding a heavy machine along a roadworks seam or a white line only for one tyre to want to wander to the left and the other tyre wander to the right - and then they randomly change over. That is the classic symptom of tyre mismatch.

Sorry I can't comment about the tail light.

The tires should fit, just check the widths on the bike.

The integrated tails can brought on Amazon or Ebay, tons of options, some with blinkers built into taillights too.

Just make sure you buy LED lights, their tons brighter.