Alternating Parental Custodianship - 50/50 Custody - Form 8332

My ex-wife and I have 50-50 joint legal and joint physical custody of our son. There is nothing in our divorce agreement regarding taxes. To my understanding, that means that my ex-wife and I must come up with a verbal agreement regarding who gets to claim our son each year and who gets to be the custodial parent for each tax year. What we've agreed upon is that we will swap years. I claimed our son for the 2016 tax year, my ex-wife will be claiming him for the 2017 tax year, and we will proceed with this pattern moving forward.

So my base question is this: should I sign a Form 8332 and give it to my ex-wife to file with her taxes, releasing our son as dependent for the 2017 tax year? Next year, should she then provide me with a signed Form 8332 for the 2018 tax year?

What I'm concerned about is parental custodianship. We want to swap parental custodianship each year so that we are each eligible for the Earned Income Credit in our given year because non-custodial parents cannot claim EIC. But only the custodial parent can fill out Form 8332. Since we have agreed to swap custodianship yearly, it is my understanding that one of us will have to fill out Form 8332 each tax year, depending on whose turn it is.

Here are some of the resources that led me to this conclusion:

https://www.irs.gov/pub/irs-pdf/f8332.pdf

https://ttlc.intuit.com/questions/3458389-who-gets-to-cliam-the-kids-when-its-50-50-custody-but-the-...

https://ttlc.intuit.com/questions/1833320-i-share-50-50-custody-of-our-son-who-gets-to-claim-him

Any insight that you might have into this problem would be much appreciated!