The only options that I see are:

PGSQL_CONV_IGNORE_DEFAULT  - Do not use DEAFULT value by removing field from returned array
PGSQL_CONV_FORCE_NULL - Convert to NULL if string is null string
PGSQL_CONV_IGNORE_NOT_NULL  - Ignore NOT NULL constraints

These are constants, so don't quote them or anything.

There is a problem when using interval.
If in the array 
"time_pause" => '00:30:00'
and time_pause is an interval
the insert fails
pg_insert(): '00:30:00' does not match with  '^(@?[ \t]+)?((([-+]?[ \t]+)?[0-9]+(\.[0-9]*)?[ ...

I've found "options" possible values:

PG_CONV_CHECK - check only
PG_CONV_STRICT - raise warning for non fatal error
PG_CONV_QUOTE - add quote around values for vchar, text datetime.
PG_CONV_SLASH - add slashes if it needed.
PG_CONV_NULLCHK - check values are defined for NOT NULL fields.
PG_CONV_NO_DEFAULT - ignore default value even if value is empty string.

Another thing that's not well documented is that (as of PHP 7.0/7.1) pg_convert doesn't like non-scalar types and will fail (but not throw just emit an E_WARNING and return false) if you pass it anything other than a string or a number, including an array or something like a DateTime. If you want to insert those types, you actually have to convert those yourself.

Also, somewhat surprisingly, $table_name is not compatible with the output of pg_​escape_​identifier, or seemingly any other kind of escaping.

This will only apply the appropriate escaping and such appropriate for embedding the PHP value into an SQL statement.

It does (by default) check for nulls when the column is marked NOT NULL, and it will complain about trying to convert strings for an integer column (floats will be truncated).

Beyond the barest checking of syntax, however, it does NOT verify that the given value is a legitimate value for the column type.

<?php
// Assuming smallints.smallintis a smallint (-32768..32767) type column
foreach([-1234,
    1234,
    0,
    32767,
    -32768,
    32768,  // bogus value for smallint type
    45.8,   // gets truncated to 45
    400000, // bogus value for smallint type
    ] as $smallint)
{
    $tmp = ['smallint' => $smallint];
    $vals = pg_convert($dbconn, 'smallints', ['smallint' => $smallint]);
    echo $vals['"smallint"'],"\n";  // Notice the column name is also made SQL-safe
}

// Assuming uuids.uuid is a UUID type column
foreach(['a0eebc99-9c0b-4ef8-bb6d-6bb9bd380a11',
    'A0EEBC99-9C0B-4EF8-BB6D-6BB9BD380A11',
    'a0eebc999c0b4ef8bb6d6bb9bd380a11',
    '{a0eebc99-9c0b-4ef8-bb6d-6bb9bd380a11}',
    'Invalid Not-a-UUID',
    '{a0eebc99-9c0b4ef8-bb6d6bb9-bd380a11}',
    'a0ee-bc99-9c0b-4ef8-bb6d-6bb9-bd38-0a11',
    ] as $uuid)
{
    $tmp = ['uuid' => $uuid];
    $vals = pg_convert($dbconn, 'uuids', ['uuid' => $uuid]);
    echo $vals['"uuid"'],"\n";
}

?>

All of the above data values will be "converted" - even the invalid ones - without complaint.