Shellac.
Different repair techs use different pad glues. Most contemporary saxophones and clarinets are padded using a form of hot glue, not too dissimilar from the hot glue used in arts and crafts. There are many commercially available products from the band instrument suppliers, all variations on the basic theme. I was originally trained using shellac, then went through a second apprenticeship using hot glue. When I started running my own shop, I quickly switched back.
From the Votaw catalogue: “For many years shellac was the standard adhesive for woodwind pad installation. Although recent developments in thermoplastic (hot melt) glues, such as our Surduzstick, provide many desireable qualities for pad work, there are still technicians who prefer the working characteristics found with shellac. Likewise, some players discern a more favorable tonal quality as a result of using shellac, and also find a more firm, defined tactile response on key closure provided bt the harder shellac over the more pliable thermoplastic adhesives.”
I take the shellac sticks, break them up and run them through a coffee grinder (dedicated to this purpose, never to grind a bean again.) The resultant powder is easily measured out using a specific set of spoons to lay the glue into the key cup. More precise than just melting the stick into the cup, and often less messy. I got the idea to do this from George’s Glue, available from Kraus music products
From the grinder: “Not suitable for use in human consumption [DO NOT USE] -use only with shellac.