WAU re-signed Mostert on a multi-year deal in June, but is yet to confirm Fullwood’s future with the team.
Fullwood’s best result this year remains a fifth-place finish at the season-opening Repco Mt Panorama 500.
He slipped from seventh to 17th in the standings after the third round in Tasmania.
Fullwood clawed himself back to 15th in the championship after a strong finish of sixth at The Bend Motorsport Park.
He outqualified and outraced Mostert in the Townsville opener, but despite two top 10 starts in the second weekend, race results went begging.
Despite Fullwood's inconsistency, Walkinshaw said WAU wasn't giving up on the 2019 Super2 champion.
"It's always easy to point the finger at a young bloke coming into an incredibly competitive category like Supercars and expect him to shine right from the start," said Walkinshaw, who is currently in his home in South-eastern France.
Fullwood scored a Tailem Bend podium in 2020
"To be honest, I think Bryce is a great driver and he's done some really, really good work for us and got himself on the podium last year.
"This year has been a bit of an up and down season, and he'll be the first to admit that.
"We're still working pretty hard in the background to try and make sure in the back-end season we will see some improvement for him.
"I think having a bit of a break we've had is going be a good thing for him and his side of the garage because it gives him a little bit of time to get a bit of a monkey off their back and reset a little.
"There's a lot of work has been going on back at the workshop, simulation, and so on to try and iron out some of the issues that we've had there.
"I'm quietly confident that we'll see a much stronger back-end of the season for Bryce."
WAU sits fourth in the teams' standings, mostly off the back of Mostert’s strong performances - but Walkinshaw believes the team now has the ingredients to be consistent championship contenders.
"There's no silver bullet to this," Walkinshaw explained.
"It's finding all the little one-percenters now, we've pretty cut down a lot of the low hanging fruits and improved significantly over the last couple of seasons.
"There's no doubt that Triple Eight and even Shell V-Power have got some really good performance that and going to be hard to beat.
WAU celebrates Mostert's Darwin win in June
"Now it's about fine-tuning what we have, we're pretty happy with the package that we've got, and we have a good engineering team.
"Now it's just all the hard work in the background to keep creeping up.
"We will keep working hard and keep believing in ourselves, there's a lot of belief in us now which is something we've not had a lot of in the past.
"Keeping that morale and confidence going is also critical.”
Walkinshaw is expected to return to Australia ahead of the Repco Bathurst 1000 in November, pending travel restrictions.