I don't know if I may have broke the system but this worked for me..

Get on your birdy and hover around the snake you like, it will aggro and follow you. Take to slightly safer location then just stay hovering above snake.

After a few minutes it will lose aggro and go to leave. DO NOT MOVE just drop the fertilised eggs from YOUR inventory DO NOT drop eggs from you birdies inventory or it will glitch.

And bam you now have snake. I hope this helps :D

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