Assuming the SQ lounge is a *G lounge, you could have accessed it if you had *G. However, since you are "only" flying C, you can only access the lounge where BR has agreements with. Which of course might be SQ's, but the only way to be sure is to ask BR (either at check-in or beforehand).

Searching on the *A website for SIN-TPE, C ticket with BR, and M&M FTL gives me access to the TG lounge and to a contract lounge. Not sure how you searched to get access to the SQ lounge.