I got it working - though missed some of your great suggestions while working on it.
The final working code is:
$result = mysqli_query($link,
"(SELECT * FROM table_1 WHERE MATCH($field1) AGAINST('$keyword1*' IN BOOLEAN MODE))
(SELECT * FROM table_2 WHERE MATCH($field2) AGAINST('$keyword2*' IN BOOLEAN MODE))");
All the parenthesis were messing me up and not using " at beginning and end instead of ' (as SpacePhoenix said). The results are now being displayed correctly.
My problem for another day relates to the actions possible with the results. Since the records are from different tables - how do I ensure that a download link, for example, pulls from the correct table? I'll have to have some fun with making the table_names dynamic in the script.
Thanks for your suggestions and help, Cheers.