Why select the transponder to TA only in the case of engine failure?
The TA mode is selected when there is an issue, basically telling the 'other' aircraft that you cannot maneuver if a RA situation occurs. The other aircraft has to do all the maneuvering (as they can still generate RAs).
From Eurocontrol ACAS II bulletin from Dec 2012:

In the TA-only mode,the equipment still performs the surveillance function (i.e.  it  scans  for  proximate traffic) but it will only generate TAs. Other TCAS II aircraft can still generate uncoordinated  RAs  against  the  aircraft which has its TCAS II in TA-only mode.
The TA-only mode may be explicitly specified in operating procedures as a response to in-flight malfunctions such as an engine failure with consequent aircraft performance implications or a pressurisation system failure followed by an emergency descent.