We are not aware of any time limit that Virginia has on taking unpaid traffic violations off of your record. If you would have paid the ticket, thus plead guilty and paid the fine for the reckless driving charge, then the reckless driving conviction would have been put on your record and then removed after the time period the DMV allows for this to remain on a driver's history.

According to the VA violation points listing on their DMV site most reckless driving convictions stay on your driving record 11 years while other traffic offenses such as speeding only stay on a Virginia MVR for 5 years.

Normally no matter what state you are in if you do not pay the ticket or appear in court to take care of the traffic violation in a different way then it remains "on the books" and may affect your license (in the way of a license suspension, etc) until you finally do take care of the violation. If your Virginia license is being shown as ineligible then it appears your license is invalid in VA and must be cleared up and reinstated before California will allow you to obtain a CA driver's license.

According to the Virginia traffic courts, in certain traffic cases if you fail to pre-pay the fine and costs (when allowed) and also fail to appear in court, a separate warrant may be issued against you on the new charge of failure to appear. You then will have to stand trial on that charge, as well as the original charge.

If you fail to appear in court, you may be convicted in absence, issued a higher fine, and possibly have your license suspended. There will also be a trial in absence fee. Failure to pay will result in license suspension. A license suspension is normally reported to the National Drivers Register (NDR) which all States have access to.

Ultimately it appears that you will need to check with the Virginia DMV to find out how to rectify the situation and get your Virginia license reinstated so that you acquire a California license.