Would jobs which ask for 3yr employment history for references contact older jobs too

So like say for example I apply for a job which requires vetting and they ask for my previous 3 years of employment, and for the last 3 years I worked at River Island. Before River Island, I worked at another place which unfortunately I got dismissed from (constantly being late). Now, in my vetting form, I won't declare the other place because it does not come under my previous 3 years of employment as I worked there before River Island. Would my new employer/vetting team still contact my former job before River Island and subsequently find out about my dismissal, or would they really just only contact the place where I've been employed for the past 3 years and wouldn't go any further back?

If you are being vetted, it's not generally for what you've done, it's for your honesty. So don't bother about this situation. They will vet what they want to vet (they don't disclose the details, for obvious reasons). If they come back to you and ask why you were dismissed, you tell them it was for poor time-keeping and that you have learnt/grown up/adapted or however you want to characterise it.

Again, vetting is less about trivial problems like this (though a prison sentence might be an issue, or dismissal for fraud) and more about honesty.

I get that, but my point was would they still manage to contact my old job prior to River Island even though it's been more than 3 years ago and on the vetting form it only asks me for my last 3 years of employment history, or do they genuinely only check just the past 3 years and don't go any further than that