I've seen mention in various places, including a quick search of Bavli Sanhedrin, that when the torah doesn't specify a method of execution in a capital case, the method is strangulation. I see a lot of discussion in Sanhedrin about priorities among the four methods and which are considered gentler, but I couldn't find anything there about how we know about (a) strangulation at all or (b) that it's the default. Is this just a "given" in the oral law, or is there a stated source or explicit reasoning somewhere? If so, what is it?
1) Rav Yoshiya: Since it is unspecified, it must be the easiest (קל) of deaths. (The Bavli explains this means the easiest of the four deaths known through tradition, following the opinion of the Sages (Mishna Sanhedrin 7:1) that strangulation is the easiest of the court imposed death penalties.)
2a) Rav Yonatan (Yerushalmi): Though we can't give him one of the stricter death penalties, because it is unspecified, we will still give him the stricter of the easier death penalties. (Rav Yonatan must hold like the opinion of Rav Shimon (Mishna Sanhedrin 7:1) that strangulation is more strict than beheading.) (This version of Rav Yonatan is possibly based on a scribal error; see Mareh haPanim and compare to the version in the Bavli below.)
2b) Rav Yonatan (Bavli): Any unspecified death must be strangulation. Rebbi Yehuda haNassi elaborates: unspecified death is used for heaven-imposed punishments (ex. Gen 38) and for court-imposed punishments. Just as heaven-imposed punishments do not leave a mark on the body, so too the court-imposed punishment must be imposed in such a way as to not leave a mark on the body. This is strangulation.
The Rambam (Hilchot Sanhedrin etc. 14:1) lists the identity of strangulation as "learned from the mouth of Moses", ie. a tradition.