To easily tame, get a Drake. Collect rock Drake eggs. Find a basilisk. Put down a bulbdog away from the Basilisk, then put a foundation over the bulbdog. Put a bunch of eggs on the foundation. Go aggro Basilisk by dismounting then remounting Drake. Run past foundation and Basilisk will aggro on bulbdog. Won't be able to kill it. Will attack until it tames. If you need more eggs, throw them from your inventory while on the Drake. Just walk right up. Super easy and doesn't take up real estate and you can tame where you need to.
Seems like raising a rock drake 1st will help you tame these. 1st raise a drake. 2nd collect a bunch of rock drake eggs. 3rd find a basilisk and while riding the cloaked drake drop the eggs one by one and it will eat them.
Actually the Basilisk only eats Rock Drake fertilized eggs. The wiki says that it should also eat other fertilized eggs, but currently it ignore them. Probably it's a bug, for now feed it Rock Drake eggs
3 min 30 second feeding interval it seems. I have better taming effectiveness by keeping it aggroed while running it in circles. Lvl 20 only took 2 eggs. Lvl 85 took 4. Drop 1 egg. Aggro. Let it feed. Start stopwatch. When ready to feed it rears up n screams but does not spit
Get yourself a Rock Drake, Karkinos, Spinosaur or any other creature usually ignored by this creature, dismout to gain its attention and mount again; Drop the Rock Drake Egg from YOUR inventory and proceed to circle the Basilisk until it looses interest on you. Wait for the feeding interval to end, repeat.