The former Notts County manager watched on as the Shaymen beat Hartlepool 2-0 on Tuesday and they followed that up with another point on Saturday.
The draw took Halifax five points clear of the bottom three and Fullarton hopes his side can now take the momentum from their last two results into the game against Sutton United next weekend.
“I’m obviously delighted,” the boss told the club’s website. “It also helps getting a result away from home and it is a follow up from Tuesday night when I was fortunate enough to be involved. So again, all credit to the players.
“You come away from home to such a physical side, some of their players were 6ft 2ins. They played very direct and we showed our attitude in abundance to deal with that today.
“We were not exposed at all, which is great credit to the players. We worked on it this week, trying to stay in the game at all times
“Any time you get a point away from home and more importantly a clean sheet, it really gathers momentum and belief and allows us to focus on the next game which is Sutton at home.”
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