Start & Stop are examples of system real-time messages, these are ‘standard’ MIDI commands that all devices may or may not support - this will be indicated usually in the manual and historically would’ve appeared in a midi implementation chart that showed whether a device sent and/or received these messages
System Exclusive messages are recipient specific - so in order for Elektron or any manufacturer to respond to a sysex string it’d need to be a declared command - and to be honest, there’s no sense in Elektron formulating a system Exclusive way to start and stop their sequencer when a standard way exists - typically System Exclusive messages are used for dumps or for parameter settings that for one reason or another aren’t best catered for by CC or NRPN or RPN midi messages etc
The Elektron Boxes do respond to sysex, but sysex handling is no longer documented, that’s left to the realms of those prepared to reverse engineer bulk dumps - or for a device which sends out sysex for a parameter change just monitoring the midi data
There is a sysex dump for device status settings, things like which page is selected and which mode the device is in, but whilst there may be a slim chance that this catch-all ‘status’ sysex message contains a reflection of the transport state I can assure you it will probably be well outside the realms of what you are trying to do and the tool you are using - to use this meaningfully (that’s if transport state is even part of that dump) you’d first of all have to know what the other settings were first, before sending back a modified version - basically, in practical terms, forget about it
Plus, unless the pedal manufacturer tells you how to input a variable parameter you’d only be able to send fixed sysex strings - so e.g. a device’s ARP is toggled by a simple known sysex string, then you’d use the whole message either turning it on or off (unless it (unusually) acted like a toggle in the system)
It’s a nice add on for a controller manufacturer to incorporate this, but it’s not going to help you do what you want here (nor for any other gear I expect, unless they made a sysex command to toggle transport and declared it)
The best way for you to program a sysex message, should the need arise, is to record to a midi monitor the string a device sends when you change a sysex parameter
However, for your purposes, probably best to ignore it - interestingly the list above doesn’t declared transport or system real-time message support, perhaps you just enter FA and FC respectively for start and stop in the sysex box (although these are not ‘exclusive’ commands)