You said that the twilight covers Apr-May, which is only two months. You get four days per week, so that equates to ~32 days to golf within the two months for ~$9.38 per round (best case playing every day). Even if you played 50% of the available time, it would cost you $18.76 per round (given the after 6 PM limitation, that would for 9-holes). Now, if it is somehow for four months as you stated, then the cost per round is a lot cheaper. If the course is half-way decent, and you enjoy paying it, then it is an oppty to consider. Again, the after 6 PM condition means that playing 9-hole rounds will be the most likely scenario, making it $37 for 18-holes (not a tremendous bargain unless it is a great course in your area).
Does the membership include use of the practice facility, or cart, or other benefits?
Twilight memberships can be great deals, but it depends on whether the course hosts a lot of leagues, tournies, etc. which will impact your available playing days. My primary course has such a membership, but until mgmt made a slew of changes this season, it was not a great deal because leagues got in the way almost every day (unless you enjoy three hour 9-hole rounds).