There is no way during the installation, or in post configuration to install Edgesight on a website other than the Default Web Site in IIS.

Install Edgesight into the Default Web Site.

Export the site configuration with the following command:

%SystemRoot%\System32\inetsrv\appcmd list site "Default Web Site" /xml /config > edgesight.xml

Edit the XML file to just include the Edgesight configuration and configure for the new site e.g.

<?xml version="1.0" encoding="UTF-8"?>
<appcmd>
    <SITE SITE.NAME="Edgesight" SITE.ID="2" bindings="http/*:8080:" state="Started">
        <site name="Edgesight" id="2" serverAutoStart="true">
            <bindings>
                <binding protocol="http" bindingInformation="*:8080:" />
            </bindings>
            <limits />
            <applicationDefaults />
            <virtualDirectoryDefaults />
            <application path="/">
                <virtualDirectoryDefaults />
                <virtualDirectory path="/" physicalPath="C:\inetpub\wwwroot" />
            </application>
            <application path="/edgesight40" applicationPool="DefaultAppPool">
                <virtualDirectoryDefaults />
                <virtualDirectory path="/" physicalPath="C:\Program Files (x86)\Citrix\System Monitoring\Server\EdgeSight\SiteRedirect" />
            </application>
            <application path="/edgesight" applicationPool="Edgesight">
                <virtualDirectoryDefaults />
                <virtualDirectory path="/" physicalPath="C:\Program Files (x86)\Citrix\System Monitoring\Server\EdgeSight\Pages" />
                <virtualDirectory path="/Temp" physicalPath="C:\Program Files (x86)\Citrix\System Monitoring\Server\EdgeSight\Data\Temp" />
            </application>
            <application path="/edgesight/setup" applicationPool="Edgesight">
                <virtualDirectoryDefaults />
                <virtualDirectory path="/" physicalPath="C:\Program Files (x86)\Citrix\System Monitoring\Server\EdgeSight\Pages\setup" />
            </application>
            <application path="/edgesight/rsproxy" applicationPool="Edgesight">
                <virtualDirectoryDefaults />
                <virtualDirectory path="/" physicalPath="C:\Program Files (x86)\Citrix\System Monitoring\Server\EdgeSight\Pages\rsproxy" />
            </application>
        </site>
    </SITE>
</appcmd>

Create the new site with the following command:

%SystemRoot%\System32\inetsrv\appcmd add sites /in < edgesight.xml
SITE object "Edgesight" added

In IIS Manager:
- Expand Default Web Site
- Right click on the edgesight application and select Remove from the context menu
- Right click on the edgesight40 application and select Remove from the context menu

In IIS Manager:
- Select the new Edgesight site
- Select MIME Types under IIS in the Features View
- Click Add in the right pane
- Enter .zpd for the File Name Extension
- Enter application/x-ms-download for the MIME Type
- Click OK

If changing the port/servername ensure Agents have the following two keys updated:

[HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Citrix\System Monitoring\Agent\EdgeSight\4.00\NetAccess]
"ServerName"="edgesight"
"ServerPort"=dword:00001f90