Just use a razor bladed scraper remove off the timber and let it be.
Attic wood leaking sap.
Amber or rosin is great if you save it and use it for stuff like stickum on tools etc.
While there are complex chemical components found in tree sap it s easy to compare sap to blood.
You can try removing sap with several different cleaning techniques but there is a chance it will come back.
It probably got hot enough in the attic and it melted out this happens over time through many heating and cooling cycles.
Turpentine works perfect for this purpose and it will not damage the quality of the wood.
When it dries it hardens and becomes difficult to remove creating unsightly spots or bumps in the wood surface.
These materials slow the leakage by clogging the wood grain pores but will not stop it completely.
Similarly when a tree is damaged the sap can bleed out.
Sap is just sugar and water.
Much of the wood produced for framing lumber has pitch pockets or areas of crystalized resin.
Usually if the wood is properly kiln dried it bakes away.
Like kevin said the attic heat restores this to a liquid form and it flows out.
Use a coarse plastic sponge to scrape the oozed resinous compounds and go over the surface of the wood with a clean towel.
Sap can caused a problem on decks and in houses where wood beams are used for support.
The sap when in live trees carries nutrients throughout the tree that helps to keep it alive.
The reason it is leaking out of the wood there is because it looks like there was a particularliy resinous knot in the pine.
Treat the knot areas with extra coats of the finishing material.
Hopefully not on your hands as you steady your walk through the attic.
Amber is fossilized resin.
When it is wet it is sticky and can rub off on clothing or attract dust and dirt.