Since Bloodseeker was changed massively in 6.82, I need to revise my earlier post about support Bloodseeker. In fact, he is now so much better as a jungling support. Here's a quick summary of the changes:
His first skill, Blood Rage, is now a combination of the old one and Bloodbath. It's now a buff that can be cast on both enemies and allies, heroes and units. The target deals percentage based bonus damage with everything (i.e. not just right clicks) but also takes bonus damage. When a unit under Blood Rage kills an enemy, they regain 25% of the enemy's HP pool as healing - likewise, if they are killed, the killer gets 25% of their HP pool as healing. Because of this change, Bloodseeker is now a much stronger jungler, as the healing is much higher now on level 1, and it also grants bonus damage, allowing him to clear camps quicker. As long as you make sure to have the buff enabled whenever you deal the killing blow, jungling is a piece of cake. Chokepoint jungling is still recommended. If facing multiple enemies, it's best to cast this on your target instead of yourself, as the other creeps would otherwise also deal bonus damage to you.
His second skill, Blood Rite, is mostly new. The silence from old Blood Rage is now inflicted by this skill, but it's shorter. However, it also has a huge area of effect and deals pure damage, but with a significant cast delay. This skill needs some setup, obviously, but it's a strong nuke and it can be used to zone out enemies efficiently even should they be able to avoid it. Naturally you can set it up using Rupture but it's even better if your team can provide some setup. His third skill, Thirst, is the same in principle, but now provides a gradual bonus instead of using a threshold, which means every bit of missing health now counts. The vision threshold has been reduced to 30%. Rupture now lasts practically forever (ok, 12 seconds), but it has no initial damage. It's still more or less the same skill. Town Portal scrolls are still the bane of his existence.
So, how does all this change things?
First of all, you only need one skill point for jungling, since level 1 Blood Rage will suffice easily. I would leave it at one point until the other skills are maxed, as it scales pretty badly, and percentage based bonuses are not too hot in the early game. Since you can cast it on a target, you can allow all of your team to make use of the bonus damage - just remember that the target will also be dealing bonus damage to all of you. You can also use it on your carry like the old version. Instead of silencing them, you'll put them in higher danger however - so don't just throw it out when your Sniper is getting whacked by the enemy's Phantom Assassin. As for what to max first, I'm divided between Blood Rite and Thirst. As a support it's generally better to max your nukes, but Blood Rite has pretty bad scaling. If you need the longer silence and have some setup to land it, go for it. However, even a level 1 Blood Rite has a lot of potential as a zoning tool, and Thirst has very good scaling.
As for items, Mekansm is no longer viable on Bloodseeker because of the increased mana cost. This is somewhat unfortunate, as you could have built a pretty fast mek with the changes to Blood Rage. The only way to sustain a mek and your other skills would be to build Arcane Boots, but it doesn't really sound all that hot. Instead, you might want to pick up a Force Staff - for all the reasons mentioned earlier - or as a new suggestion: Eul's. You can use it to cancel those pesky TPs, run even faster and setup your Blood Rite on a target (heroes with blinks, leaps and similar abilities can still get out). Diffusal Blade or Rod of Atos can be useful too - Diffusal is still probably better, but Atos does make you tankier. Blade Mail is still strong. Another note about Blade Mail: if you make a habit of casting Rupture on Blade Mailed targets, getting a Black King Bar might be smart. Or, you can also Eul's yourself when they start to run.
As for the game plan, it's mostly intact. Go to the jungle, but don't just afk there. Once you have a level in each of your abilities, you can easily gank lanes (remember to carry those TPs!), or even save a teammate with a zoning Blood Rite. You might even want to leave it at 1 and max Thirst, and then just play mind games with it as enemies are still very likely to try and avoid it. All in all, I think support Bloodseeker is now fully legit if you just jungle and roam, and build some utility items.