I'd keep it simple and use a small diameter 'hidden' vertical hole: Drilled on the inside of the stock, (where it is radiused for the action).

The hole would go through the glued piece and into the main stock.

Fill the hole with a 'pin' made from a Finish or 'serrated' nail (head cut off) and 'gooped up' with 'Acraglas'.

Make the pin short enough, so that it is recessed into the wood.   

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