I'm eligible for a Rep. Ireland passport.   If you alternated between two passports each time you got a new visa, would this work or are the 2 passports electronically linked etc?

Likely to be linked in the past - and especially now that biometric is happening at entry points.  The IO seeing less consecutive activity at first-glance might make them less likely to dig deeper, but ...

 

The primary advantage is alternating passport when applying for Visas at nearby consulates, who look at what they see in the passport, vs Immigration's database of one's full Thai-entry history.  

 

But, you can only "switch passports" in the air, and even then not flying into Laos from Thailand, per some reports.   The Thai consulate where you apply will usually want to see the entry-stamp to that country in the passport where they are putting a new Visa, so you need to enter the neighboring country on the passport you will be using to apply.

1 hour ago, SamuiAddict said:

I'm eligible for a Rep. Ireland passport.   If you alternated between two passports each time you got a new visa, would this work or are the 2 passports electronically linked etc?

Not anymore, due to better control.

+Maybe  the Irish Embassy still do income letters, for extensions (if needed),  that would save having to spend on transfer fees to move money, frequently to your Thai bank?

-Dual nationality perhaps not a good thing if you are routing through Malaysia I was told, Daughter left her Thai passport in the UK when She and Hubby went there.

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1 hour ago, SamuiAddict said:

I'm eligible for a Rep. Ireland passport.   If you alternated between two passports each time you got a new visa, would this work or are the 2 passports electronically linked etc?

Work? What are you trying to achieve?

 

You can use either passport to enter the country, but they are likely to get linked so you cannot hide your past entry history if that is what you are trying to achieve.

Just one of the reasons biometric screening was finally implemented. 

 

In the future, it will be at all boarders, and new passports / numbers will not be able to hide your entry history.