awk -f error message sometimes prints wrong line

[Shlomo]

Using Gawk 5.1.1:

$ cat a.awk

BEGIN {}
{
$ awk -f a.awk
awk: a.awk:3: B
awk: a.awk:3: ^ unexpected newline or end of string

Note the error message mentions line 3, but the "B" seems to come from line 2.
When writing the program inline, the error message is good:

$ awk '
> BEGIN {}
> {'
awk: cmd. line:3: {
awk: cmd. line:3:  ^ unexpected newline or end of string

If I change the first line to be non-empty, I get a different error message:

$ cat a.awk
{}
BEGIN {}
{
$ awk -f a.awk
awk: a.awk:3: (END OF FILE)
awk: a.awk:3: ^ source files / command-line arguments must contain complete 
functions or rules

But this error message too doesn't print the contents of line 3. Writing the 
program inline gives a good error message:

$ awk '{}
> BEGIN {}
> {'
awk: cmd. line:3: {
awk: cmd. line:3:  ^ unexpected newline or end of string