The 20-year-old was named on the bench by head coach Gregor Townsend in the 24-13 victory over Treviso last Saturday but didn't make it on to the pitch.
But the Canadian international winger says it's just a matter of time before he gets his chance, and he's eager to make it count.
Taylor told the Evening Times: "I am desperate to gain some experience in the RaboDirect PRO12 and it would be great to be heading home on the back of a run-out for Warriors against the Dragons on Friday night.
"I knew when I came here it would take time to establish myself and that patience would be important. It was great to make the bench for the Treviso game, although a bit frustrating not to get on.
"But Gregor has been very good with me and given me a lot of encouragement, and I know that I still have a lot to learn and to develop as a rugby player.
"But it would be great to make my debut at home against Dragons as Scotstoun is a great venue and I'd love the chance to show what I can do."
Taylor has been playing for Dundee HSFP, but with an international break just around the corner he wants to return to top class domestic action.
The Canucks' youngest-ever player to win an international cap is set to lock horns with Samoa, Russia and New Zealand Maori in the autumn internationals.
"They are three big games for us and everyone knows how physical and tough Samoa and the New Zealand Maoris are. But Russia will also be a really tough challenge for us," he added.
"Hopefully I will get plenty of game time, but it has been good to get five or six games under my belt with Dundee.
"The last thing you want as a rugby player is to be training all week and then not getting any game time. So I feel like I am pretty sharp and I'm just hungry to make my debut."