Learn Spanish (Latin America): Ojalá hubiera pitado antes.

Hubiera pitado is the past perfect (pluperfect) subjunctive. When combined with ojalá, it expresses a regret or an impossible wish about the past (I wish it had beeped). If you used the imperfect subjunctive (ojalá pitara), it would mean a wish for the present or future (I wish it would beep).

Since this lesson is about sí que, could I add it here to emphasize that I wish it HAD beeped?

You wouldn't use sí que in the same clause as ojalá. Sí que emphasizes that something is actually happening in reality, whereas ojalá sets up a hypothetical, unreal wish. You could use it in a follow-up phrase, like: Ojalá hubiera pitado antes. ¡Sí que nos habría salvado! (I wish it had beeped earlier. It sure would have saved us!)

Does pitar only refer to electronic machines beeping?

No, pitar is a versatile verb. While it means to beep (like a microwave or an alarm), it is also the standard verb for honking a car horn or a referee blowing a whistle in sports. In context, this sentence could just as easily mean 'I wish the referee had blown the whistle earlier.'

Would it be correct to say hubiese pitado instead?