Maybe a sign that it's times for a break ?.
Sometimes it helps to 'speak out your code' to determine if it makes sense. Have a look at that line. tableofcontents_table, I assume, is your Profields Table. Reading that out loud, your code is saying, find me siblings (PLURAL) of this page and get me the value of its (SINGLE) tableofcontents_table field. Doesn't sound right, does it? It's like saying 'find me 10 oranges (PLURAL) and show me its (SINGLE) price. That's wrong. The question would be, which orange's price? We have 10 oranges here! It should read, 'find me 10 oranges (PLURAL) and show me their (PLURAL) prices. Aha, so, we are dealing with a collection. Any collection has to be iterated (foreach) to get each members individual value. Alternatively, you could ask for the first(), last() or nth() orange to deal with one member only.
OK, so I need to get some sleep too. The docs say this about $page->siblings():
$toc is a PageArray.
If you run this in Tracy console:
<?php
d($page->siblings("template=tableofcontents")->tableofcontents_table);// null
You will get the value null, hence your error message since you are doing this null->render().
Now for some unsolicited advice ?.
TracyDebugger is your best friend.
The table clearly is there and clearly is a sibling and its template is as stated and the table also. Whilst this might be the case, it is best to always check if your selector/query returned something (and its type) before you start working with it.
Hope this helps.
ps: Profields Table has its own VIP support forum, accessible to you if you have a current subscription