Well, Body ECU would not be my first suspect for this exact symptom set. The circuit does transit the B-ECU but they are just straight traces--probably fixable if they ARE the problem, which I doubt. The exception is the Flash relay, but that can be swapped separate of the B-ECU. Thing is, the turn circuit uses the exact same cross-connections on the B-ECU, so if it was bad for one, it would be bad for the other. A B-ECU is wildly expensive new, so you are talking junkyard. It is not that hard a swap, but it's a lot of plugs and wires. I'd go to some effort to rule everything else out, before I went that way.
My first suspect would be the Hazard Switch, as in it is not returning control of the circuit to the turn circuit when cycled to off. Play with it enough, and it restores the Turn circuit. It's really the only thing that is different between the two circuits.
Key question is does the green-red wire between the hazard switch and the flash relay have 12V+ when Hazard is OFF and key is ON. If it does not, Hazard Switch is your culprit. If it does, then I would try a new flash relay before I swapped the whole B-ECU.
Actually, I'd do a whole lot of other things before I swapped the B-ECU.
OP does not give year (Grrrr....) so here is 2002 EWD. I think other years are the same.
http://tacoma.site40.net/4Runner_96-02_Repair&Wiring/techinfo.toyota.com/ileaf/ewdtmc2/ewdtmpdf/ewdsourc/2002/024runne/systemci/022tshwl.pdf