Actually, both separated (みそ{HL}じたい{HLL}) and compound (みそじたい{LHHLL}; fall on じ) accents are heard, though the latter is arguably colloquial. The same applies to ~自身.
There is no apparent tendency in usage as I observe, except that the separated accent sounds more like an emphasis, so it is (slightly) more suitable for saying "the very —" than "— proper". (The same effect can be achieved by stressing 自体 when there is no accent change.)
When you use the compound accent, the last accent block before 自体 is under its dependent scope, which is the last noun or everything after the last verb/adjective.
脱出を考えなければいけないこと自体
In this case, いけないことじたい{LHHHHHHLL} usually makes one accent phrase.
flat + じ⤵︎たいconsidered acceptable by your acquaintances (excluding cases where the first noun is inherently flat)? – naruto Apr 05 '21 at 16:32