Support Zil's not that common these days, but then neither is Zil himself. He was one my first favorite champions, and still is, but I haven't touched him in a good while. He's still good in the support, the only issue being that most people would see him on a team and think his potential is wasted without all the farm of being mid. For his bombs to remain relevant he needs a decent amount of AP, so its harder to funnel as much gold into wards on him as you should for a support.
You basically run a Zill support lane very similar to a Leona or Sona support lane (minus Sona's sustain). Aggressive and constant pokes. Your bomb range is stupid long, especially with bush control and a quick time warp. And as you observed, a free resurrection is support gold. You can tower dive, bait to your own tower, nullify a gank, etc. And time warp itself is an amazing support utility. By late-mid game you can permanently effect 1 target with time warp and just a little CDR. By end game you can keep it going on two targets. In lane you can basically double the gank potential of your lane through the combined efforts of your bomb harass and time warp's ability to either speed your teammates to a target or lock the target down, situationally! It's a very fun lane. The biggest issue Zil has is against a good heavy sustain like Soraka or Taric, who can heal through non-fed Zil's bombs and even counter harass/zone you very well.
Rune wise you build similar to AP Carry Zil, only it may be worth replacing quints/seals with GP5. You're not a tanky support, your a harass/utility support, so it's a tough call on the mp/5 or AP runes and the GP5. Magic Pen reds and AP/lvl blues seemed to work best for me, though.
Masteries are probably best at 9/0/21. You want the mpen, CDR, and gold mostly, and if you use heavy harass mregen as well. Zil support may be one of the few champions I'd recommend clarity on in certain situations because of how much you want to spam your bombs and time warp + bomb combo.
Itemwise you obviously can't afford the RoA which is standard on AP Mid Zil. He builds alot like standard support. Wards, wards, wards, philo into Shurelias (SUPER speed boost!), maybe even a chalice in there like Sona. Late game frozen heart isn't a bad goal against a good AA enemy team either.