I didn't get the validation that the sensors are working though because I didn't get a "alls good" beep when turning the key.
Do you even know if the buzzer (or warning module) works like it is suppose to in your system yet?..........hmmm, what if it doesn't work at all? Shouldn't you test it somehow? What if the oil goes low and you have no clue the module or the sensor even works? What if the buzzer isn't good out of the box? Or goes bad down the road? Or you hooked it up wrong? Or the power wire to the buzzer fell off?
I'm pretty sure you actually should get a "self test/all is well" at power up.......It not only says "all is well" it also says to you "your warning module is okay", "your beeper and the power and ground path are all okay" too!!..........
This is why the "all is well/self test" is important to hear
each time you power up, anything can happen/break/fall off/corrode/open, if not today, maybe tomorrow, you should always hear/listen for this before each outing.......
It's sorta analogous to your "lamp test" when you first turn and
each time, your car's key to turned on, all the lamps light up for a sec so you can see/check none are burnt out, thus you'll know if something goes wrong you'll know at least the lights are going to be able to light up to alert you..........
Double check the module actually works and should or shouldn't do a "self test/all is well" and at least, ya might want to simulate low oil to assure that the low oil sensor, module and the buzzer all work....for this one time at the very least to be safe.
If that is the case is their a way to test it to see if it's sending a signal before I purchase a new tachometer?
Do you have a frequency function on a multimeter? If not, use the AC setting on a multimeter and you should see at least 10, 20, 30VAC or higher on the gray wire when running the motor.