I'm pretty sure they are not related.
The clicking blinker noise even though the turn signals are not on is usually caused by a bad turn signal switch.
The check engine light will require a little more home work. You wil need to pull codes from the computer. You can do this by buying an inexpensive code reader, calling your local parts stopre to see if they can pull codes for you, or bringing your vehicle into a shop to have a diagnosis done.
Once you know what codes you have post them here along with an engine size and I'll do my best to help.
Let me know if you have any questions and I'll do my best to answer them. Thank you for using FixYa.com!
I’m happy to assist further over the phone at https://www.6ya.com/expert/jeremy_d728a59f986299fa
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