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I would thin it with about 20-25% mineral spirits... that way it will penetrate and hopefully not leave a sticky gooey surface... If it looks like it will be sticky etc., brush on a second coat of just mineral spirits to spread it around.... or just live with it...
Last minute change of sealing plans... I found Agralife Timber Seal and it looks really good... non-toxic and even food safe. Excellent looking product with great reviews. I found it on Home Depot's website and since they don't stock it at my store I had them ship it to the store. Not too bad of a price... $39.95 for a gallon. The product has great specs that are hard to ignore... I am sure the linseed oil would be fine, but wanted to step it up a notch.
My father in law had a 5 gallon bucket of brick red oil based exterior paint. So in a couple of hours of painting, we have preserved the walk-in smoker for decades.