We thought we had an absentee Fholder - no ground rent demanded for several years, nobody knew where he was, etc. It caused all sort of problems with the purchase, and we started the FH purchase process onnthe assumption that he was absent.
In fact he was hiding just few miles away under another name, because of debts attached to the FH.
The process would have been simpler if he hadn't eventually decided to,pop up. In the case of an absentee, It goes to a tribunal, who decide via a formula (based on value of,property length of lease and ground rent) how much you will have to pay.
Do use a solicitor who knows what they're doing! We started the process with the High St sol.who'd handled the purchase, , but they were frankly pretty useless. I eventually found a specialist sol. online. They were miles better but It still took around a year, and it still had to go to a tribunal even though Mr Debt-Dodging Fholder had revealed himself by then - thinking there'd be money in it.
Although our FHolder had not demanded ground rent since we'd bought the flat, nor from the previous owner (he pretended he'd sent invoices but it was a lie) we still had by law to pay him 7 years' ground rent before the FH transfer could be finalised.
I think there's a 7 year limit, so I would suspect that you might also have to pay it, even if you haven't been invoiced. In the case of an absentee, the FH price is put into an (escrow?) account, in case the FHolder ever pops up, so,presumably the same might be done with back GR.
I have a feeling that you are required to show the court that you've done your best to trace the FHolder. I did use a tracing service for ours, fully expecting them to say they couldn't find him (it was thought that he'd returned to his native country) but despite the name change they found him in about a week!
IMO you need to speak to a specialist solicitor. I found ours courtesy of google, and until the actual court sessions (2, IIRC) it was all done by phone/email, so it didn't need to be a local firm. There was also a free 15 minute initial consultation by phone.