I'm guessing boiled linseed oil would work better than linseed oil
at room temperature, but never tried it or heard of it being used.
Traditionally piano techs would take the pins out and varnish the holes
and/or add sandpaper.  Many old piano hacks would even use the back
of the tuning "wrench lever" to hammer in the pins (which is why it's
called a "tuning hammer" to this day).  Why?  I don't know.  What most
piano technicians are using these days to "dope" pinblocks is thin
viscosity cyanoacrylate adhesive [CA or "Crazy Glue"].  The "glycerin
stuff" (which had been most popular) swells the wood but also weakens it.

At this time of year I don't "dope" pinblocks.  My theory is that when
it's humid, the cells in the wood are full of moisture.  If I try to
put any liquid around the pins, I doubt it would penetrate much (if at
all) beyond the bushing and even if it did, it would not displace the
water -- all it would do is create a barrier where any future attempts
to use a liquid tightener would not seep past the bushing and just make
matters worse.

This time of year, I tap the pins in a little (the coils should not
touch the plate) and replace with larger tuning pins where needed.
I let the customer know they may need me back in the winter for
treatment with thin viscosity CA adhesive.

I always offer the more expensive remedies as options.  I wrote a feature
article in the PTG Journal about "repinning" with larger tuning pins
and I do many re-stringing jobs with new pin blocks as well.  I always
tell the customer that these are the best way to solve their loose
tuning pin problem.  More often than not, the "general piano owning
public" will go with the more cost effective approach.  The combination
of tapping pins, replacing with larger tuning pins and thin viscosity
CA adhesive will solve the problem of loose tuning pins in the vast
majority of instances for many years.

Bill Maguire