diff --git a/core/time/new_spec.rb b/core/time/new_spec.rb
index 91ce4b2e3..0cde11c98 100644
--- a/core/time/new_spec.rb
+++ b/core/time/new_spec.rb
@@ -570,6 +570,23 @@ def obj.to_int; 3; end
       }.should.raise(ArgumentError, /missing min part: 00 |can't parse:/)
     end
 
+    # These strings end exactly at the byte where the parser expects a ':', so
+    # the message has no offending byte to append. The other error cases here
+    # all carry a trailing zone, which left that boundary unexercised.
+    it "raises ArgumentError if the time string ends where a ':' is expected" do
+      -> {
+        Time.new("2020-12-25 00:56")
+      }.should.raise(ArgumentError, /\Amissing sec part: 00:56\z|can't parse:/)
+
+      -> {
+        Time.new("2020-12-25T00:56")
+      }.should.raise(ArgumentError, /\Amissing sec part: 00:56\z|can't parse:/)
+
+      -> {
+        Time.new("2020-12-25 00")
+      }.should.raise(ArgumentError, /\Amissing min part: 00\z|can't parse:/)
+    end
+
     it "raises ArgumentError if the time part is missing" do
       -> {
         Time.new("2020-12-25")