The documentation is wrong, the time zone offset is parameter #23 not #24. (See the definition of PARAM_TIMEZONE in params.h.) Note also that it's a Parameter, not a Feature.
The format of the time zone offset is hour:minutes, with negative hours for time zones east of GMT.
For PDT, you want to set parameter #23 to -7:00.
As far as I know, there's isn't a convenient way to set parameters by SMS. Notice there is no documented PARAMS command. There is an undocumented PARAMS command, but it requires you to send a list of all of the parameter values starting with the miles/km (so parameters 2 through 23, 22 strings including the crazy ACC configuration strings).
The best way to set the time zone offset is through the iPhone or Android app.
View attachment 75615
For people who aren't using an iOS or Android device, it would be nice to have a PARAM command that works like the FEATURE command, or a dedicated command for setting the timezone offset.