The engine was driven from Larne fire station at about 04:00 GMT on Saturday and crashed into cars and houses a short time later.
Robert Duffin, 66, from Green Link in Larne, appeared at Coleraine Magistrates' Court on Monday facing five charges linked to the incident.
Ross Clarke, 19, from Fairway in Larne, also appeared, accused of 14 offences.
He faces charges including burglary, aggravated vehicle taking, causing damage and various motoring offences.
The pair were remanded in custody to appear again on Thursday at Ballymena Magistrates' Court, when it is expected a bail application will be made.

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Chris Kane struck six minutes from the end in Perth to claim a hard-fought 1-0 Scottish Premiership victory against Inverness Caledonian Thistle.
It was only their second success in the last 12 league matches but was enough to move them on to 39 points - level with fourth-placed Ross County.
"Overall we are having not too bad a season," said Wright.
"I mentioned to the players that we are now just two points worse off than we were this time last season.
"Hopefully we build on this now as I think we deserved the win."
Saints, who have nine games to play, were made to wait for their win with David Wotherspoon having a penalty saved by Owain Fon Williams shortly before Kane's winner.
"I thought we looked more likely to score but we have missed a few penalties and I feared the worst when that happened," Wright said.
"But fair play to David as he didn't let that get to him and he had an excellent game and contributed in the build-up to the goal."
Caley Thistle manager John Hughes reckons his team were responsible for their own downfall in a game they finished with just 10 men.
Captain Gary Warren was sent off in the second half for two yellow cards, the second of which was for conceding the spot-kick.
"I said to them at half-time, 'only one team can beat you here and that's yourself' and that's what happened," said Hughes.
"There's no way we can feel sorry for ourselves. If we had kept 11 players on the park we might have got something.
"I was a little bit disappointed that even with 10 men we couldn't see the match out and get a draw.
"St Johnstone have thrown the kitchen sink at us and we nearly got the draw even if we lacked a bit of penetration up top.
"We were trying to hang on a bit after Gary was sent off and he was just caught out a couple of times.
"I really feel for the boys as they put their bodies on the line but it didn't work out after putting in so much effort.
"Especially for the goalkeeper as Owain made a great save and I thought at that point it might be our night but it wasn't to be."
The Highlanders remain ninth, five points clear of the relegation zone and three points off the top six.
"It is very tight in the league at the moment and it is going to be nip and tuck right until the split," added Hughes.
"We do still want to get into the top six and while we have had a hard programme there are no excuses.
"There is still a lot to play for this season and I am hoping to have more numbers to pick from in the weeks ahead."
Two men have been remanded in custody over the theft of a fire engine in County Antrim.
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Tommy Wright insists St Johnstone are on course to equal last season's points tally of 57 despite a recent poor run.