What is the statute of limitations to file a Class C traffic ticket appeal in County Court?
In 2002 the Defendant pled guilty in JP Court but never paid the fine.
In 2012 an attorney filed an appeal in county court.
Did the statute toll or not?

10 days. Your guy is loooooong past that. See CCP 45.0426(a). The appellate court lacks jurisdiction unless an appeal bond is filed within 10 days of judgment being entered. Not paying the fine just means he is delinquent, not that the appellate clock didn't start ticking.

The JP Court yesterday said he pled guilty, however the file shows his guilty plea was for the appeal.

Thus, he did nothing from the time of the ticket in 2002 to the time he filed an appeal & entered a plea in 2012.

Is the statute of limitation run to file the appeal?

So nothing was done on the ticket for 10 years? He was never issued a FTA or paid anything, nothing? I'd be filing a motion for speedy trial, not an appeal.

The statute of limitations is tolled by the filing of a formal complaint. If no formal complaint was filed then the statute of limitation of two years applies. If he pled guilty in 2002 and the defendant failed to perfect the appeal then you issue a capias pro fine. If a formal complaint was filed and he entered his plea 10 years later then the only problem was a speedy trial violation. Statute of limitations is an affirmative defense to be raised by the defendant. I am confused how you would have a 10 year old ticket with no action on it. (Not to say I haven't seen that happen in J.P. Court--just it shouldn't)

If he entered a guilty plea in JP court, regardless of his motive, he is guilty, period. Now if he entered a nolo plea and was found guilty in JP court, he would have ten days to perfect his appeal to county court. If he didn't perfect his appeal in that time frame, the judgment of the JP court stands. In order to perfect an appeal, you have to post the appeal bond. He didn't do that for ten years? Pay up.