I'd like to vote on my alt account so I can buy a pet. Is there any issue with this if I wait 24 hours after my last vote on my primary account?
As long as you only vote once per 24 hours, you are fine. (Vote only goes through if you progress to Gtop and verify the captcha) Just in case you are using a different IP address and might experience an overlap before 24 hours have elapsed, first try voting on the same account you voted yesterday (on royals website). If it shows "~ minutes remaining", you still need to wait for 24 hours to pass. If it shows [click here] link, that means 24 hours have passed. Click back to the royals website voting page and vote with the alt account.