So we can conclude that the catalyst has basic sites that relate to Bronsted Basic and Lewis Basic sites, or acidic sites that relate to Bronsted Acidic and Lewis Acidic sites.
Inverse gas chromatography, where the solid subtrate to be studied is the packing of the column and various gases with base and acid characteristics are used as mobile phase. By changing systematically the temperature and the mobile phase and measuring the retention time you can get a lot of information of the alkalinity/acidity of your adsorbent. Several review articles and books are available.
first dont say Bronsted Basic and Lewis Basic sites this concept only for the acid sites.
any way it very dificult to find such reaction which exclusively catalysed by any specific site. you have to get idea from TPD and FTIR using some prbe molecule; eg you can use NH3 or pyridine for acid site and CO2 for basic site.
another method also is there ie Hammet indicator method. the reaction result may supported your preveous result or you can corelate.