I Just Won A Small Claims Case Against My Neighbor. Do They Need A Reason To Appeal It Other Than Losing?

Location: California.

I'm going to include the background below for those who are curious, but I just received the judgement from the small claims court proceeding where I sued my neighbor over not paying for a shared fence. In the letter it states the award is on hold pending any appeals.

From what I'm reading, my neighbor doesn't need a reason to appeal other than "I'm mad I lost" and they can simply appeal and get another shot at overturning the judgement in my favor. Is this correct? Or do they need to cite a reason why they disagree with the ruling to get an appeal? It seems to me they should have a reason why they feel it was unjust other than "I just don't want to pay that." If they do appeal, and I win again, do I get damages or anything for having to take more time off to go back to court?

Background: I had to sue my neighbor because our shared fence needed replacement, and they refused to pay for it. Our fence was 20+ years old, showed signs of dry rot and decay, and they sent me a letter saying they were going to replace some boards and to put our dogs away so they can do work on the fence. We told them we weren't comfortable with this, and we wanted to get a quote from a reputable fencing company. We had an assessment done, and they determined the fence to be in dire need of replacement, as it was rotten, falling over, and a hazard. Furthermore, we had a shared chain-link fence which my neighbors displaced by building an 8 foot privacy fence on the property line without my consent, so the fence company told us we needed a site survey done as well. My wife and I paid $1,600 for the surveyor, and then we asked the neighbors to split the cost of a shared fence.

Their response to this was to hire a lawyer, who said the fence was in "excellent condition" and he shared pictures of the fence from my neighbors, which shows that they just painted their fence red (which covered the rot and decay). The lawyer said they are in no way responsible to pay for half, as it's a good condition fence and we're replacing it for cosmetic reasons. We sent them a response saying we disagree, and have documentation from a fencing company saying it is in need of replacement, and sent them pictures of the decay. We gave them a 30 day notice before work began, and they did not object. The new fence went in, and I sent them an invoice, they didn't respond. After 2 months of no contact, I filed to sue them in small claims court and won a judgement this week. Before the trial we exchanged discovery, and I gave them the receipts, pictures of the rotten fence and the displaced chain-link fence, and the letters that were sent back because they refused delivery.

They're discovery however claims that I acted unilaterally without their consent to replace the fence, they claimed that I had it replaced "while we were on vacation without our consent" (even though I provided them with a 30 day notice which they did not object during that time) and they said that I "stole" their property, being the privacy fence they constructed on our shared property line. It's also important to note this fence was 8' tall, and local ordinance in our city says that fences along the sides of a property have a max height of 6'). We presented these to the judge, who looked at my pictures, listened to them say they didn't feel they should pay the full amount, and that they offered me $500 towards the fence as they felt this was all they should have to pay. We got a judgement within days of trial, despite being told it would take 4 - 6 weeks.