How to remove thumbs from part page and bibliography?

I would like to use thumbs but not on the part pages and on the bibliography.

documentclass[pdftex,10pt,b5paper,twoside]{book}

usepackage[lmargin=25mm,rmargin=25mm,tmargin=27mm,bmargin=30mm]{geometry}

usepackage[Glenn]{fncychap}
    ChNameVar{Largefontfamily{cmbright}selectfontcolor{black}}
    ChNumVar{Hugefontfamily{cmbright}selectfontcolor{black}}
    ChTitleVar{Largefontfamily{cmbright}selectfontscshapecolor{black}}

usepackage[height={2cm},distance={5mm},topthumbmargin={auto},bottomthumbmargin={auto}]{thumbs}

usepackage{fancyhdr}

usepackage{lipsum}

newcommand{thumbforchapter}{addthumb{Chapter thechapter}{Large{thechapter}}{white}{gray}}

begin{document}

pagenumbering{arabic}

part{Test 1}
chapter{Intro} label{chap:1}thumbforchapter
lipsum[1-15]cite{happel}

part{Test 2}
chapter{Mid} label{chap:2}thumbforchapter
lipsum[1-9]cite{happel}

chapter{End} label{chap:3}thumbforchapter
lipsum[15-19]cite{happel}

begin{thebibliography}{9}
bibitem{happel} 
Patrick Happel.
lipsum -- Easy access to the Lorem Ipsum dummy text.
2014
end{thebibliography}

end{document}

How do I restrict thumbs? Is it better to use fancyhdr?

Also, in my real code, the thumbs do not really shift downwards before the fifth chapter. I was however unable to recreate it here in this MWE.