[DOCS] EQL: Update `allow_no_indices` default (#63748) (#63891)

Co-authored-by: Adam Locke <adam.locke@elastic.co>

docs/reference/eql/eql-search-api.asciidoc

@@ -56,9 +56,25 @@ To search all data streams and indices in a cluster, use
 [[eql-search-api-query-params]]
 ==== {api-query-parms-title}
 
-include::{es-repo-dir}/rest-api/common-parms.asciidoc[tag=allow-no-indices]
+`allow_no_indices`::
+(Optional, boolean)
 +
-Defaults to `false`.
+NOTE: This parameter's behavior differs from the `allow_no_indices` parameter
+used in other <<multi-index,multi-target APIs>>.
++
+If `false`, the request returns an error if any wildcard expression,
+<<indices-aliases,index alias>>, or `_all` value targets only missing or closed
+indices. This behavior applies even if the request targets other open indices.
+For example, a request targeting `foo*,bar*` returns an error if an index
+starts with `foo` but no index starts with `bar`.
++
+If `true`, only requests that exclusively target missing or closed indices
+return an error. For example, a request targeting `foo*,bar*` does not return an
+error if an index starts with `foo` but no index starts with `bar`. However, a
+request that targets only `bar*` still returns an error.
++
+Defaults to `true`.
+
 
 include::{es-repo-dir}/rest-api/common-parms.asciidoc[tag=expand-wildcards]
 +

docs/reference/rest-api/common-parms.asciidoc

@@ -48,9 +48,12 @@ end::target-index-aliases[]
 
 tag::allow-no-indices[]
 `allow_no_indices`::
-(Optional, boolean) If `false`, the request returns an error when a
-wildcard expression, <<indices-aliases,index alias>>, or `_all` value targets
-only missing or closed indices.
+(Optional, boolean)
+If `false`, the request returns an error if any wildcard expression,
+<<indices-aliases,index alias>>, or `_all` value targets only missing or closed
+indices. This behavior applies even if the request targets other open indices.
+For example, a request targeting `foo*,bar*` returns an error if an index
+starts with `foo` but no index starts with `bar`.
 end::allow-no-indices[]
 
 tag::allow-no-match-transforms1[]