Hi John!
I may have found something that may be useful about the 5th and 6th Austrian Jäger battalions of the Napoleonic Wars:
The 5th seemingly participated in the Russian campaign of 1812: (See "Division Trautenberg") https://blundersonthedanube.blogspot.com/search?q=austrian+jagers
The 5th and 6th were Moravian: http://www.napolun.com/mirror/web2.airmail.net/napoleon/Austrian_infantry.htm#austrianinfantryjagers
http://napoleonistyka.atspace.com/Austrian_infantry.htm#_jagers
On the Jäger's organization: https://www.napoleon-series.org/military/organization/Austria/ArmyStudy/c_AustrianArmyJagers.html
Feld-Jäger battalions of the Austrian army and their commanders: https://www.napoleon-series.org/military/organization/Austria/infantry/c_austrianinf8.html
I have not been able to find more information, at least not yet.