I recently learned of a conviction I did not admit on a UK visa application. What happens if I admit/omit it next time?

I traveled to the UK on a visitors visa a couple of years ago. At the time I had one old conviction (20 years old) for a very minor offense which resulted in a very small fine, no jail time. I admitted this on my application and as expected it was of no concern. I have since decide to apply for a long term visa with the aim of eventually moving permanently.

I applied for a Police Clearance certificate last year and to my surprise found another conviction from 2005. Also minor (a traffic offense that is also a criminal offense) which led to another small fine and no jail time. I did not know about this because I did not go to court and paid what I thought was a regular traffic fine and am now told was an admission of guilt fine leading to instant conviction (this was not information I was given at the time.)

I’ve since had both expunged and now have a clean clearance certificate. I know that since I admitted the first offense on my visitor visa application I must admit it again. I would normally have no problem admitting the second since it was also minor and more than 10 years ago. My concern is that I did not admit it last time as I honestly did not know about it and my lack of admission last time will be seen as deception even if I explain the circumstances. But I am equally worried that if I do not admit it, even though it was expunged, they may find out and deny me the long term visa.