The form for the widows pension for wife Elizabeth is on Findmypast, which indicates John died in 1835 (26th of Dec). Shows their wedding date, and her address, and that he was quartermaster in the 7th Hussars.
There might be more for him there, but there are 65 entries for John Rudd's.....BUT ! Findmypast is free this weekend, so check it out!
I don't think their newspapers are free this weekend though.... her obit is in there (1839) which indicates she was the widow of John, Quartermaster of the 7th Hussars, and left 5 orphans.
Give a shout if you can't find it!
Edit: Assuming they let you open the image for the Widows Pension Form, and not just give the transcript, keep clicking the right arrow to see the next images, which is a certified copied of their marriage, and her burial record. Note that on their marriage, he was said to be in the Dragoons, as explained by Jorose.