How to search a file for the last block of consecutive lines that contain a keyword in Perl

Imagine a text file like below where <some random text> could be anything or nothing, implying the KEYWORD can appear anywhere in the line, alone or along with other text:

 1 <some random text>
 2 <some random text>KEYWORD<some random text>
 3 <some random text>KEYWORD<some random text>
 4 <some random text>
 5 <some random text>
 6 <some random text>KEYWORD<some random text>
 7 <some random text>
 8 <some random text>KEYWORD<some random text>
 9 <some random text>KEYWORD<some random text>
10 <some random text>KEYWORD<some random text>
11 <some random text>
12 <some random text>KEYWORD<some random text>
13 <some random text>KEYWORD<some random text>
14 <some random text>
15 <some random text>KEYWORD<some random text>
16 <some random text>

How can I get the last occurrence of 2 or more consecutive lines that contain the keyword (lines 12 and 13 in the example)? To be clear, I am not interested in lines (8, 9, 10) because although they contain the keyword and are consecutive, they are not the last, nor in line 15 because although it contains the keyword and is the last line with keyword, it is not part of 2 or more consecutive lines.