Is this the corporate action you are referring to?
I am in the same boat as you and trying to figure it out.
Neither alternative should be subject to income tax (+USC & PRSI) as far as my reading of the situation goes.
If you do not sell the bonus share rights in the market, your Santander ords shareholding will increase when the rights lapse and for Irish tax purposes the newly-issued shares are deemed to have been acquired at the same date as the original holding. The original cost will be shared between the original shares and the bonus (newly-issued) shares. In your spreadsheet where you record your holdings, just increase your share position from 5,500 to 5,739 approx after the rights lapse. (I'm assuming you hold approx 5,500 shares (550/0.10) currently). Your stockbroker will automatically reflect this on your account. Also adjust your cost per share. Total consideration is unchanged.
If you sell the bonus share rights in the market, I
think for tax purposes it is a deemed part-disposal of the shareholding in respect of which the rights were offered. So, this may or may not give rise to a chargeable gain in 2020. To calculate your chargeable gain you need to deduct the 'allowable cost' from the sales proceeds of your rights. Allowable cost = original cost of holding x [proceeds of rights sale / (proceeds of rights sale + market value of remaining shares)].
If the result of this formula is an amount less than your rights disposal proceeds, you have a chargeable gain, but you also have a €1,270 annual exemption as well to set against this. If the result is a larger figure than your rights disposal proceeds, then you have no chargeable gain.
Given the amounts involved, there is probably no tax for you to be concerned about for 2020 if you sell the rights.
That's my analysis of it and how I will approach the taxation of it - but willing to be corrected. I'm not tax-qualified, just a DIY investor with a copy of the ITI Capital Taxes manual to assist in computing taxes for corporate actions.
Also, I think that technically it is not a dividend/scrip dividend as they are precluded from this due to ECB recommendations.