What is the syntax rule for having trailing commas in tuple definitions?

Another advantage of trailing commas is that it makes diffs look nicer. If you started with

a = [
    1,
    2,
    3
]

and changed it to

a = [
    1,
    2,
    3,
    4
]

The diff would look like

 a = [
     1,
     2,
-    3
+    3,
+    4
 ]

Whereas if you had started with a trailing comma, like

a = [
    1,
    2,
    3,
]

Then the diff would just be

 a = [
     1,
     2,
     3,
+    4,
 ]

It is only required for single-item tuples to disambiguate defining a tuple or an expression surrounded by parentheses.

(1)  # the number 1 (the parentheses are wrapping the expression `1`)
(1,) # a 1-tuple holding a number 1

For more than one item, it is no longer necessary since it is perfectly clear it is a tuple. However, the trailing comma is allowed to make defining them using multiple lines easier. You could add to the end or rearrange items without breaking the syntax because you left out a comma on accident.

e.g.,

someBigTuple = (
                   0,
                   1,
                   2,
                   3,
                   4,
                   5,
                   6,
                   7,
                   8,
                   9,
                   10,
                   #...
                   10000000000,
               )

Note that this applies to other collections (e.g., lists and dictionaries) too and not just tuples.

In all cases except the empty tuple the comma is the important thing. Parentheses are only required when required for other syntactic reasons: to distinguish a tuple from a set of function arguments, operator precedence, or to allow line breaks.

The trailing comma for tuples, lists, or function arguments is good style especially when you have a long initialisation that is split over multiple lines. If you always include a trailing comma then you won't add another line to the end expecting to add another element and instead just creating a valid expression:

a = [
   "a",
   "b"
   "c"
]

Assuming that started as a 2 element list that was later extended it has gone wrong in a perhaps not immediately obvious way. Always include the trailing comma and you avoid that trap.