first i am primarily playing in small groups so my advices are tinkered around my needs while doing so.
my current spec
changes nearly every few hours
as you can see alot of the skills are quite similar to yours
differences:
1. backlash is completly useless beside marking an assist target
2. so my advice woud be a substitution for dark flare as it is in most cases the most reliable heal debuff in game
3. skipped both rest staff heals as they are pure zerg skills i´ve reslotted them with
4. harness magica as long as it refills "unlimited" magica while having dots ticking on you or beeing casted at it is THE magica management option for templars
5. reflective light - snaring your opponents is quite handy to allow your team mates chasing them more efficiently while doing slightly dmg numbers aswell.
6. change of the ultimates
a) sturdy horn is a pure zerg ability -> switched it with soul assult one of the hardest hitting singeltarget abilities to enable you to increase the pressure on on target tremendously
b) shooting star - even though nova offers more ae dmg the cc part of it is a lot stronger and its fire and forget usage is slightly faster than having to place a ground target my reason against any of rite of passage morph is its limit of 4 allies heals per tic wich is on top compleatly random so its not even usefull in zerg situations and limited efficiancy in small scale situations.

I run with 2 bars both Resto Staff, one bar is dedicated to full healing. The other dedicated to support/debuffs.

My debuff bar looks like this:
1) Breath of Life
2) Binding Javelin
3) Reflective Light
4) Total Dark
5) Dark Flare

U) Soul Assualt

Healing Bar
1) Breath of life
2) Efficient Purge
3) Immovable
4) Blinding Flashes
5) Radiant Magelight

U) Solar Prison

I use a Resto staff on both bars. Heavy attack when you are not casting to regen magicka. I also run full Cloth armor for the magicka cost reduction from Evocation.

Currently I am running 5 piece Seducer, 3 piece Way of the Arena. All jewelry I have has reduced spell cost. I use infused trait on my chest and helm with health enchants, everything else is impenetrable with magicka enchants.

Try to keep immovable up as much as you can, you will find that as soon as people recognize you as a healing templar, you will get most of the attention from the dps. Generally my first cast when we start a fight is to cast immovable, then heal as needed, if you get melee attention hit blinding flashes to cut the mdps coming in on you. Radiant magelight is under used but I truly think it is the better morph, remember to recast it if you ever switch bars.

I do not run Blazing shield, annulment, or shield stack, I find those to be utterly broken mechanics and I don't want/need to take advantage of something broken to be competitive in PvP.

I generally only run in a small group of max 3-4 people.

You absolutely, 100%, want Radiant Magelight (morph of Inner Light from the Mage Guild tree) on your healing bar. You want as many heals to crit as possible.

As others have said, 7 light is probably best, with a focus on spell power. This allows you to switch very easily between dps and healing (Templars can easily do both).

As for the skills: Blazing Shield is excellent. Anything with "Blazing" in the name is excellent. Blazing Spear is one of the best skills in the game, period.

Backlash, Rune Focus, Eclipse, and Blinding Light are *** in pvp. Just utter and complete ***.

Cleansing Ritual is good, but Efficient Purge is better. Restoring Aura is awesome, and both of its morphs are incredibly useful -- Repentance is one of the best pvp skills in the game.

If you're doing support, you should also have Rapid Retreat on your bar.

Focus on Blazing Shield and Spear, whenever beeing attacked by vamp-groups or fotm DKs, pop your Blazing Shield and try to stay in their range. It is one of the best ways to counter the 1vsX players when you are not alone. You'll often see a DK chasing into a zerg and popping all his AE fotm stuff + permanent root (Talons). Here you need rapid manauver if you want to move. Instead, if you want to fight go for Shield + Spear AE dmg.

There are really many players atm (and since June) that use and abuse specific specs that can be countered with blazing shield (not by trying to heal the dmg).

Beside that, try out to be minimalistic on healing: Try just using breath of life (+healing springs for ultimate-reggen out of fight) and going into your own survivability. A dead Templar or a CCd templar (bacause he has not enough stamina) is no helpful templar.

Remind u that actually Bow is the preferred weapon which also offers a heal-debuff which you have to remove from your team mate who will not use purge himself or push "x". Against heal-debuffs 1-2 purge(s) are necessary before healing (e.g. under meatbag fire). Therefore you loose important time for healing -> find a non-templar purge char. I know - most of the time we do it - but for effective healing it's better s.o. else does it, so you can start immediately to push out your 1500+ heals.

Repentance IMO is not "one of the best skills" but very nice in combination In PvP if another templar uses the other morph. I prefer the other morph because 80% more stamina reg means really everbody in the group can keep Immovable up. Beside that you can keep up rapid maneuver, Caltrops, etc. pretty easily AND sprint all the time, especially to be faster at healing sb.

I call them "group buff(s)" skills -> as a Templar life is much easier if another mate uses maneuvre, another one purge, etc. Basic logic: every team member uses one "group buff / skill". Very often Templars handicap their hotbar by taking too many group buffs inside and leaving other important skills out, loosing their ability to self-defend. Do not make the same error if you have a regular group, assign roles to certain chars: like purge, so that you can heal instantly up!