It appears that title changes when both the seller and the buyer sign the reverse side of the vehicle registration certificate.
While a vehicle registration with the government is prima facie evidence that a vehicle is owned by the person indicated in the register of the transportation department, Section 140(2) of the Finance Act (1992) under which Ireland's current vehicle registration system was established effective January 1, 1993 (ignoring grandfathered cases) states that this is a rebuttable presumption of ownership only.
Nothing in the regulations issued pursuant to the Finance Act states otherwise, and there is language in one of the forms reproduced in a schedule to the regulations which seems to state that registration is something that one must do promptly upon a change in ownership, rather than change of ownership being something that only actually happens upon a change in registration.
This is a deviation from the common law that was subsequently codified in the law of sales for untitled tangible personal property, in which title transfers upon delivery of the goods, or if it is covered by a document such as a negotiable warehouse receipt, upon deliver of a negotiated (i.e. signed) warehouse receipt. Likewise, the historical rule for transfer of real property before ownership registration was established for it, was "signed, sealed, and delivered" meaning that a deed had to be signed by the seller, notarized, and delivered to the buyer or the buyer's agent, for title to be transferred.
Generally speaking, when property is represented by an ownership certificate or is intangible, transfer of the certificate or relevant document, rather than physical possession, governs transfer of title (before real property records were formalized and bureaucratized, one had to deliver constructive possession of real property with "livery of seisen" by handing over a rock or dirt or twig from the real property to the buyer to signify delivery of possession of real property, the modern equivalent of which would have been to hand over keys to a building).
But, the Finance Act and the associated regulations and forms seem to make clear that you need to have both parties, rather than merely the seller (under this historical rule and the rule in most U.S. jurisdictions), sign the relevant form to transfer title.
The question is, at what point does the car actually become mine? The
reason I ask is that my insurance policy covers me to drive a car of
the specified registration (not the one I just bought) and any other
car not owned by me. So if I own the car the moment I hand over the
money, I am suddenly not insured to drive it home! But if I own it
when the government dept. process the form (or when the seller posts
it), I probably have a day to get in touch with the insurance provider
to change the coverage to the new car (e.g. if the sale is outside of
My suspicion is that this issue is addressed not by the time that title transfers itself, but by a clause in a standard form car insurance contract in Ireland. There is probably a "tail" provision that extends the previous owner's insurance coverage until the registration is processed if it is processed within a reasonable time. But, I don't have the full text of an Irish car insurance policy contract at my disposal to review in order to confirm that fact.
You could probably read the terms of your current car insurance policy contract, if you have one, and determine the answer, as this is likely to be effectively uniform for all car insurance policies in Ireland.
Or, as @chepnor notes in the comments, "if you call your insurance company ahead of time and tell them you will be purchasing the car. They'll tell you how to ensure you are covered."