Battery and Oil pressure lights keep coming on

[A872B]

94 180sx sr20det

So I replaced my alternator but my light still comes on sometimes. When the light is on, I have 14 volts. Even while I'm driving. It comes and goes.
Also, while driving, the oil pressure light will come on too. I pulled over, turned the car off and turned it back on and the light went off. It seems to be an intermittent issue as well. There is no change in the engine sound and there is no signs of lack of oil pressure.

Is there a reason why I keep getting these warning lights? Is there anything I should look into first? Not sure where to start with this car

[tunermt]

Sounds like you already have a way to monitor voltage which you confirmed holds 14v even when the battery light comes on?
Unless there is a wiring issue/bad connection at the alt for the voltage reference the battery light should stay off. (the bat. light acts as a resistor for the alternators voltage reference point, without that little LED inline the alt does not see the signal it needs and will not charge. **very common issue on non nissan chassis using 90s nissan engines.**
Check all the connections at the alt and clean all of your grounds in the engine bay/add a ground from the alt body to the engine block and engine block to negative battery terminal (not just to chassis ground).

The oil pressure light coming on would be of more concern and just like you did with the voltage i would recommend getting a proper oil pressure gauge on the engine to check and ensure there is indeed no oil pressure. (obviously an oil pressure issue will damage things quickly).

[macgiver]

With alternators , suspecting and changing them - ALWAYS have your 'suspect' one bench tested at parts store(s)
note: MORE THAN ONE !
On the tail-end ALWAYS have that 'new' replacement even , checked at parts store(s) - MORE THAN ONE .

Helps in the Loooooong run , ya know