Hi Sascha,
Did you add the new searching parameters for searching accounts for your requirement?
Based on experience, BADI BADI_CRM_BUPA_IL_SEARCH only called from method FILTER_BY_SEARCH_CRITERIA of class CL_BUPA_IL_HEADER_SEARCH.
Kindly please refer to documents in http://wiki.sdn.sap.com/wiki/display/CRM/How+to+add+an+existing+field+to+a+search+page+of+a+different+component
The document is very helpful.
Hopes it helps.
Cheers
eddhiek