It depends on what type of jungler you prefer to be.
Glasscannon Shaco, non Bruiser Rengar, Kha'Zix etc, your job is to kill the enemy Carries. Your team shouldn't have more than 1 assassin against a tank composition (because too many assassins means that the enemy team can just walk over to you because you lack a front line ), so you take out the enemy carry (and go back before everything collapses on you). Taking out the carry means that they won't have anyone capable of destroying YOUR frontline so your team can easily follow up. Master Yi falls in this, mid game.
Rek'sai, Volibear, Rengar, Kha'Zix (provided they actually build some defense), your job is part assassin part tank. Should you engage? Yes. Should you stay and do damage? Maybe. Should you try to kill the backline? Not really. Your job is to disrupt. You go in, preferably into the carries to force the enemy frontline to actually come down on you (and this is why you must have defense), and keep them there so your own team can follow up on your engage. Once that's done, you should either peel for your carry (since he'll be most likely near the enemy tanks/bruisers/assassins) or try to disrupt the ADC so they won't attack your own frontline. If you're getting too low, back to your own backline and just peel if you can, else, go back, try to heal (If fighting near a jungle camp, just do the camp to regain some HP), and go back in to mop up.
Sejuani, Amumu, Nautilus. You're going to fight as equals. You are a tank, they have a lot of tanks. What you want is to outplay the enemy tanks. If you have a good way to engage in your team, you should be trying to bait the enemy team into a position where your team can engage well (just walking up to them may do the trick). If not, and you're the one who should engage, you're screwed. If your team doesn't have any more tanks, you either have to engage and tank 5 because your team can't afford to tank, or you engage and the enemy team's frontline goes into your own team. But there's nothing you can do, except creating picks if that's the case. If you know you can't teamfight, try to catch the enemy alone, and then teamfight, or just stall the enemy team while someone splitpushes.
Tryndamere, Master Yi. Your job is simple. Get items. Mid game, play like an assassin, try to take kills, else just wait for an engage and then go in and back out before you're in risk. Late game, you're an attack damage carry. If your team can hold their ground without fighting, splitpush. Get turrets and then fight (the enemy will usually be sending someone to you, so if you join your team when the enemy splits, you have an easy fight). If not, it's alright. You're a monster. Wait for an engage from either team (preferably yours). Jump right into the enemy carries, you'll probabbly 1-3 shot them. Depending on your health, proceed to the bruisers/assassins and then the tanks.
This means that fighting a tank team is dependant on you having the capability to nullify their damage output (shutting down their carries) or avoiding the fight completly and search for alternative ways to win the game.
Good picks against tank teams are not really that viable in the jungle. The best thing to kill a tank is an ADC, but ADCs struggle in the jungle. Something that does help a lot is percentage damage, a Liandrai's Torment (Magic) or a Blade of the Ruined King (Phisical) are good against health stacking tanks, but then again, it does depend on your role. However, there are junglers who have % damage in their kit, Sejuani and Amumu are two great examples. Combine them with a Liandrai's and you have something that will help damage the tanks (if your ADC can put them low enough with your help, it's a won fight, unless your own tanks are dead)