You have not shown how you generate the value of $viewState, which is pertinent here. However it won't make any difference since you define the value of $param in single quotes, meaning $viewState won't be interpolated anyway.

You also are using the most inconvenient way of building and making your request. Consider using at least HTTP::Request::Common, if not something simpler such as HTTP::Tiny.

Sometimes sites are just so anti-scraping that you can't get there with LWP. This seems to be one of them. I don't think your problem is your proxy. I couldn't retrieve the page via LWP either. I am able to get search results using cURL with the same args: try running this from your command line and see what you get:

curl -L 'https://patentscope.wipo.int/search/en/search.jsf' -H 'Host: 
+patentscope.wipo.int' -H 'User-Agent: Mozilla/5.0 (Macintosh; Intel M
+ac OS X 10.11; rv:53.0) Gecko/20100101 Firefox/53.0' -H 'Accept: text
+/html,application/xhtml+xml,application/xml;q=0.9,*/*;q=0.8' -H 'Acce
+pt-Language: en-US,en;q=0.5' --compressed -H 'Referer: https://patent
+scope.wipo.int/search/en/search.jsf' -H 'Content-Type: application/x-
+www-form-urlencoded' -H 'Cookie: JSESSIONID=CD31D066DF8710F9FE9B5C9C5
+397A977.wapp1nC' -H 'Connection: keep-alive' -H 'Upgrade-Insecure-Req
+uests: 1' --data 'simpleSearchSearchForm=simpleSearchSearchForm&simpl
+eSearchSearchForm%3Aj_idt379=FP&simpleSearchSearchForm%3AfpSearch=bru
+shless+motor&simpleSearchSearchForm%3AcommandSimpleFPSearch=Search&si
+mpleSearchSearchForm%3Aj_idt447=workaround&javax.faces.ViewState=7923
+733300114075152%3A8489940171963107341' | grep 'Tokyo Parts'
[download]

I don't know how long the tokens will be good for. That command will probably stop working after some time.

You may have to move up to WWW::Mechanize (which handles cookies) or even Selenium::Remote::Driver (which handles JavaScript).

Hope this helps!

update:: add mention of Mech, thanks Corion...