The Listed Andrew Ramsden Stakes (2800m) at Flemington on Saturday is restricted to three, four and five-year-olds and offers the winner a 'Golden Ticket' into the Group 1 Melbourne Cup (3200m) at Flemington in November.
Eustace said he likes the idea of the race and giving up-and-coming stayers the chance to compete for the Melbourne Cup but would also like to see the race opened up to six-year-olds.
"It works, but I don't think it should be is restricted to three, four and five-year-olds," Eustace said.
"There's plenty of good six-year-olds. Verry Elleegant's OK and I don't think being six stops you from being a good stayer."
Through Irish Eyes is a four-year-old son of Tavistock and is coming off a last start second over 2400m at Caulfield on April 16 where he beat home Thursday's Warrnambool Cup winner Witchachar Star.
Eustace said if it wasn't for the money, which offers the winner $300,000 and the Melbourne Cup ballot exemption, Through Irish Eyes would continue racing through the grades.
"If it wasn't the Ramsden and the prize money that it is, you would be happy to see him work through the grades as he's that sort of horse he is," Eustace said.
"But he's in excellent order. He had a good gallop last week and he'll have a stride up on Monday.
"He's still quite a raw horse. He looks like a three-year-old now and he's four and he is probably going to come into his own when he's five or six.
"It would suit him if he won the race as he could then have a breather. It wouldn't be a long one, but he wouldn't need a lot of racing to get back up to full fitness.
"He's a natural staying horse, a progressive stayer that likes Flemington and we would like it dry."
While entered for the race, Eustace said Feel The Rush was unlikely to run.
"I don't think she's going well enough but she loves the mud."