Actually, I went back and did find some logs.
"[Debug] Java Home: c:\program files (x86)\runemate\jre
[Debug] Java Version: 8u121 x86 (Oracle Corporation)
[Debug] Maximum Heap Size: 743MB
[Debug] RuneMate Version: 2.20.0
[Debug] Operating System: Windows 10 x64
Apr 23, 2017 2:57:51 PM java.util.prefs.WindowsPreferences <init>
WARNING: Could not open/create prefs root node Software\JavaSoft\Prefs at root 0x80000002. Windows RegCreateKeyEx(...) returned error code 5.
Please restart to auto-update or manually <a href="
Download | RuneMate">update</a>.
Please restart to auto-update or manually <a href="
Download | RuneMate">update</a>.
Please restart to auto-update or manually <a href="
Download | RuneMate">update</a>.
Please restart to auto-update or manually <a href="
Download | RuneMate">update</a>.
Please restart to auto-update or manually <a href="
Download | RuneMate">update</a>."
"
[Debug] Java Home: c:\users\spencer\documents\runemate\jre
[Debug] Java Version: 8u121 x86 (Oracle Corporation)
[Debug] Maximum Heap Size: 743MB
[Debug] RuneMate Version: 2.22.1
[Debug] Operating System: Windows 10 x64
Please restart to auto-update or manually <a href="
Download | RuneMate">update</a>."
The logs are recorded only the times I've closed the Updater before completion. Runemate opens, but cannot sign in due to update needed.